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papers

Publications (90)

cs.LG2017

Tensor Decompositions for Modeling Inverse Dynamics

Stephan Baier, Volker Tresp

Modeling inverse dynamics is crucial for accurate feedforward robot control. The model computes the necessary joint torques, to perform a desired movement. The highly non-linear in…

math.NT2016

The square sieve and the large sieve with square moduli

Stephan Baier

We give a short alternative proof using Heath-Brown's square sieve of a bound of the author for the large sieve with square moduli.

math.NT2015

Quadratic congruences on average and rational points on cubic surfaces

Stephan Baier, Ulrich Derenthal

We investigate the average number of solutions of certain quadratic congruences. As an application, we establish Manin's conjecture for a cubic surface whose singularity type is A_…

cs.AI2016

Learning with Memory Embeddings

Volker Tresp, CristÃ³bal Esteban, Yinchong Yang +2

Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a…

cs.CL2018

Improving Visual Relationship Detection using Semantic Modeling of Scene Descriptions

Stephan Baier, Yunpu Ma, Volker Tresp

Structured scene descriptions of images are useful for the automatic processing and querying of large image databases. We show how the combination of a semantic and a visual statis…

math.NT2010

Mean values with cubic characters

Stephan Baier, Matthew P. Young

We investigate various mean value problems involving order three primitive Dirichlet characters. In particular, we obtain an asymptotic formula for the first moment of central valu…

math.NT2024

Variance of primes in short residue classes for function fields

Stephan Baier, Arkaprava Bhandari

Keating and Rudnick derived asymptotic formulas for the variances of primes in arithmetic progressions and short intervals in the function field setting. Here we consider the hybri…

math.NT2006

Large Sieve Inequalities for Characters to Powerful Moduli

Stephan Baier, Liangyi Zhao

In this paper we aim to generalize the results in Baier and Zhao and develop a general formula for large sieve with characters to powerful moduli that will be an improvement to the…

math.NT2007

A Remark on the Conjectures of Lang-Trotter and Sato-Tate on Average

Stephan Baier

We obtain new average results on the conjectures of Lang-Trotter and Sato-Tate about elliptic curves.

math.NT2007

The Sato-Tate Conjecture on Average for Small Angles

Stephan Baier, Liangyi Zhao

We obtain average results on the Sato-Tate conjecture for elliptic curves for small angles.

math.NT2017

Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced version

Stephan Baier

We study the problem of Diophantine approximation on lines in $C^{2}$ with numerators and denominators restricted to Gaussian primes. To this end, we develop analogs of well…

math.RT2013

Dimensions of Ext-groups of Weyl modules for GL_2

Stephan Baier, Sergey Lamzin, Vanessa Miemietz

Let F be an algebraically closed field of positive characteristic p. The third author and Will Turner gave an explicit description of the extension algebra of Weyl modules for GL_2…

math.NT2026

Diophantine approximation with primes from short intervals

Stephan Baier, Sayantan Roy

In this paper, we establish hybrid results on Diophantine approximation with primes from short intervals. In particular, we prove the following result in a slightly modified form:…

math.NT2022

Diophantine approximation with prime restriction in function fields

Stephan Baier, Esrafil Ali Molla, with an appendix by Arijit Ganguly

In the thirties of the last century, I. M. Vinogradov established uniform distribution modulo 1 of the sequence $p I^\pm$ when $I^\pm$ is a fixed irrational real number and $p$ runs over…

math.NT2005

On the large sieve with square moduli

Stephan Baier

We prove an estimate for the large sieve with square moduli which improves a recent result of L. Zhao. Our method uses an idea of D. Wolke and some results from Fourier analysis.

math.NT2005

The large sieve with sparse sets of moduli

Stephan Baier

Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We t…

math.NT2019

A Lower Bound for the Large Sieve with Square Moduli

Stephan Baier, Sean B. Lynch, Liangyi Zhao

We prove a lower bound for the large sieve with square moduli.

math.NT2006

The Lang-Trotter Conjecture on Average

Stephan Baier

For an elliptic curve $E$ over $\ratq$ and an integer $r$ let $I ¨ _{E}^{r} (x)$ be the number of primes $p \leq x$ of good reduction such that the trace of the Frobenius morphism of $E/\fi…

math.NT2018

The large sieve with power moduli for $Z [i]$

Stephan Baier, Arpit Bansal

We establish a large sieve inequality for power moduli in $Z [i]$ , extending earlier work by L. Zhao and the first-named author on the large sieve for power moduli for the…

math.NT2025

An uncountable subring of $R$ with Hausdorff dimension zero

Stephan Baier, Shameek Paul

We construct a subring as mentioned in the title (hence this subring has Lebesgue measure zero).

math.NT2008

On Primes Represented by Quadratic Polynomials

Stephan Baier, Liangyi Zhao

This is a survey article on the Hardy-Littlewood conjecture about primes in quadratic progressions. We recount the history and quote some results approximating this hitherto unreso…

math.NT2005

On the large sieve with sparse sets of moduli

Stephan Baier

Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We t…

math.NT2026

A Bombieri-Vinogradov theorem for sectors in real quadratic number fields

Stephan Baier, Esrafil Ali Molla

We establish a Bombieri-Vinogradov theorem for sectors in real quadratic number fields.

math.NT2025

Multiple exponential sums and their applications to quadratic congruences

Nilanjan Bag, Stephan Baier, Anup Haldar

In this paper, we develop a method of evaluating general exponential sums with rational amplitude functions for multiple variables which complements works by T. Cochrane and Z. Zhe…

cs.AI2018

Improving Information Extraction from Images with Learned Semantic Models

Stephan Baier, Yunpu Ma, Volker Tresp

Many applications require an understanding of an image that goes beyond the simple detection and classification of its objects. In particular, a great deal of semantic information…

math.NT2008

On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves

Stephan Baier, Liangyi Zhao

In this paper, we obtain an unconditional density theorem concerning the low-lying zeros of Hasse-Weil L-functions for a family of elliptic curves. From this together with the Riem…

cs.SE2020

Conformance checking: A state-of-the-art literature review

Sebastian Dunzer, Matthias Stierle, Martin Matzner +1

Conformance checking is a set of process mining functions that compare process instances with a given process model. It identifies deviations between the process instances' actual…

math.NT2022

Solutions of $x_{1}^{2} + x_{2}^{2} - x_{3}^{2} = n^{2}$ with small $x_{3}$

Stephan Baier

Friedlander and Iwaniec investigated integral solutions $(x_{1}, x_{2}, x_{3})$ of the equation $x_{1}^{2} + x_{2}^{2} - x_{3}^{2} = D$ , where $D$ is square-free and satisfies the congruence condition $D\eq…

math.NT2021

Solving $p$ -adic polynomial equations using Jarratt's Method

Stephan Baier, Swarup Kumar Das, Saayan Mukherjee

We implement an iterative numerical method to solve polynomial equations $f (x) = 0$ in the $p$ -adic numbers, where $f (x) \in Z_{p} [x]$ . This method is a simplified $p$ -adic ana…

math.NT2023

Large sieve inequalities with power moduli and Waring's problem

Stephan Baier, Sean B. Lynch

We improve the large sieve inequality with $k$ th-power moduli, for all $k \geq 4$ . Our method relates these inequalities to a restricted variant of Waring's problem. Firstly, we inpu…

math.NT2020

Large sieve with sparse sets of moduli for $Z [i]$

Stephan Baier, Arpit Bansal

We establish a general large sieve inequality with sparse sets $S$ of moduli in the Gaussian integers which are in a sense well-distributed in arithmetic progressions. Th…

math.NT2012

Multiplicative inverses in short intervals

Stephan Baier

We give an alternative proof of a recent result by T.D. Browning and A. Haynes (arXiv:1204.6374v1) on multiplicative inverses in sequences of intervals and improve this result unde…

math.NT2025

Upper bounds for shifted moments of Dirichlet $L$ -functions to a fixed modulus over function fields

Stephan Baier, Peng Gao

In this paper, we establish sharp upper bounds on shifted moments of the family of Dirichlet $L$ -functions to a fixed modulus over function fields. We apply the result to obtain up…

math.NT2026

On certain bilinear sums with modular square roots and applications

Stephan Baier

We extend bounds on additive energies of modular square roots by Dunn, Kerr, Shparlinski, Shkredov and Zaharescu and apply these results to obtain bounds on certain bilinear expone…

math.NT2017

A note on Diophantine approximation with Gaussian primes

Stephan Baier

We investigate the distribution of $p I^¸$ modulo 1, where $I^¸$ is a complex number which is not contained in $Q (i)$ , and $p$ runs over the Gaussian primes.

math.NT2012

Exponential sums with Dirichlet coefficients of L-functions

Stephan Baier

Improving and extending recent results of the author, we conditionally estimate exponential sums with Dirichlet coefficients of L-functions, both over all integers and over all pri…

math.NT2022

Small Pythagorean triples modulo prime powers

Stephan Baier, Anup Haldar

Let $p > 5$ be a fixed prime. We obtain an asymptotic formula related to small solutions of quadratic congruences of the form $x_{1}^{2} + x_{2}^{2} \equiv x_{3}^{2} mod p^{n}$ where $\max\{|x_1|,|…

math.NT2009

On Hecke Eigenvalues at Piatetski-Shapiro Primes

Stephan Baier, Liangyi Zhao

Let $I^» (n)$ be the normalized n-th Fourier coefficient of a holomorphic cusp form for the full modular group. We show that for some constant $C > 0$ depending on the cusp form and…

math.NT2026

On bilinear sums with modular square roots and applications II

Stephan Baier

In this article, we continue our recent investigations on bilinear sums and additive energies with modular square roots. Here we improve our recent results for the case when the ra…

cs.CL2019

Analyzing Customer Feedback for Product Fit Prediction

Stephan Baier

One of the biggest hurdles for customers when purchasing fashion online, is the difficulty of finding products with the right fit. In order to provide a better online shopping expe…

math.NT2026

Small solutions to inhomogeneous and homogeneous quadratic congruences modulo prime powers

Stephan Baier, Arkaprava Bhandari, Anup Haldar

We prove asymptotic formulae for small weighted solutions of quadratic congruences of the form $I^»_{1} x_{1}^{2} + \dots + I^»_{n} x_{n}^{2} \equiv I^»_{n + 1} mod p^{m}$ , where $p$ is a fixed odd prim…

math.NT2017

A note on the gaps between zeros of Epstein's zeta-functions on the critical line

Stephan Baier, Srinivas Kotyada, Usha Keshav Sangale

It is proved that Epstein's zeta-function $I^¶_{Q} (s)$ , related to a positive definite integral binary quadratic form, has a zero $1/2 + i I^^{3}$ with $ T \leq Î³\leq T + T^{{3/7} +\var…

math.NT2010

A Subconvexity Bound for Automorphic $L$ -functions for $S L (3, Z)$

Stephan Baier, Liangyi Zhao

In this paper, we develop a conditional subconvexity bound for Godement-Jacquet $L$ -functions associated with Maass forms for $S L (3, Z)$ .

math.NT2024

A note on the distribution of prime ideals in real quadratic fields

Stephan Baier, Sayantan Roy

In this note, we give a summary of the article ``The distribution of prime ideals of imaginary quadratic fields'' by G. Harman, A. Kumchev and P. A. Lewis and establish analogous r…

math.NT2026

The large sieve for square moduli, revisited

Stephan Baier

We revisit the large sieve for square moduli and obtain conditional improvements under hypotheses on higher additive energies of modular square roots.

math.NT2005

On the $p^{I^} »$ problem

Stephan Baier

We deal with the distribution of the fractional parts of $p^{I^} »$ , $p$ running over the prime numbers and $I^»$ being a fixed real number lying in the interval $(0, 1)$ . Roughly speaki…

math.DS2012

Automorphisms with exotic orbit growth

Stephan Baier, Sawian Jaidee, Shaun Stevens +1

We exhibit continua on two different growth scales in the dynamical Mertens' theorem for ergodic automorphisms of one-dimensional solenoids.

math.NT2016

Restricted simultaneous Diophantine approximation

Stephan Baier, Anish Ghosh

We study the problem of Diophantine approximation on lines in $R^{d}$ under certain primality restrictions.

math.NT2026

Diophantine approximation with sums of two squares II

Stephan Baier, Habibur Rahaman

Recently, the authors showed that for every irrational number $I^\pm$ , there exist infinitely many positive integers $n$ represented by any given positive definite binary quadratic fo…

math.NT2019

Prime powers dividing products of consecutive integer values of $x^{2^{n}} + 1$

Stephan Baier, Pallab Kanti Dey

Let $n$ be a positive integer and $f (x) := x^{2^{n}} + 1$ . In this paper, we study orders of primes dividing products of the form $P_{m, n} := f (1) f (2) \dots f (m)$ . We prove that if $m >…

math.NT2008

A refined version of the Lang-Trotter Conjecture

Stephan Baier, Nathan Jones

Let $E$ be an elliptic curve defined over the rational numbers and $r$ a fixed integer. Using a probabilistic model consistent with the Chebotarev theorem for the division fields o…

math.NT2020

The large sieve inequality with square moduli for quadratic extensions of function fields

Stephan Baier, Rajneesh Kumar Singh

In this paper, we establish a version of the large sieve with square moduli for imaginary quadratic extensions of rational function fields of odd characteristics.

cs.AI2015

Type-Constrained Representation Learning in Knowledge Graphs

Denis KrompaÃ, Stephan Baier, Volker Tresp

Large knowledge graphs increasingly add value to various applications that require machines to recognize and understand queries and their semantics, as in search or question answer…

math.NT2021

On the distribution of $I^\pm p$ modulo one in imaginary quadratic number fields with class number one

Stephan Baier, Marc Technau

We investigate the distribution of $I^\pm p$ modulo one in imaginary quadratic number fields $K \subset C$ with class number one, where $p$ is restricted to prime eleme…

math.NT2011

On Hecke eigenvalues at primes of the form $[g (n)]$

Stephan Baier, Liangyi Zhao

In this paper, we study the average of the Fourier coefficients of a holomorphic cusp form for the full modular group at primes of the form $[g (n)]$ .

math.NT2021

On the distribution of $I^\pm p$ modulo one in quadratic number fields

Stephan Baier, Dwaipayan Mazumder, Marc Technau

We investigate the distribution of $I^\pm p$ modulo one in quadratic number fields $K$ with class number one, where $p$ is restricted to prime elements in the ring of integers…

math.NT2011

Exponential sums with coefficients of certain Dirichlet series

Stephan Baier

Under the generalized LindelÃ¶f Hypothesis in the t- and q-aspects, we bound exponential sums with coefficients of Dirichlet series belonging to a certain class. We use these estim…

math.NT2026

Partial progress towards the large sieve for square moduli

Stephan Baier

This paper condenses and expands upon our recent contributions arXiv:2603.00768 and arXiv:2603.25814, which belong together, producing a single streamlined manuscript. We have adde…

math.NT2017

A Polya-Vinogradov-type inequality on $Z [i]$

Stephan Baier

We establish a Polya-Vinogradov-type bound for finite periodic multipicative characters on the Gaussian integers.

math.NT2026

Small solutions of ternary quadratic congruences with averaging over the moduli

Stephan Baier, Aishik Chattopadhyay

In a recent paper, we proved that for any large enough odd modulus $q \in N$ and fixed $I^\pm_{2} \in N$ coprime to $q$ , the congruence \[ x_1^2+Î±_2x_2^2+Î±_3x_3^2\equi…

math.NT2025

Diophantine Approximation with Piatetski-Shapiro Primes

Stephan Baier, Habibur Rahaman

We prove that for every irrational number $I^\pm$ , real number $I^^{2}$ , real number $c$ satisfying $1 < c < 9/8$ and positive real number $I^¸$ satisfying $I^¸ < (9/ c - 8) /10$ , there exist infinit…

math.NT2023

Diophantine approximation with prime denominator in real quadratic function fields

Stephan Baier, Esrafil Ali Molla

In the thirties of the last century, I. M. Vinogradov proved that the inequality $∣∣ p I^\pm ∣∣ \leq p^{- 1/5 + ε}$ has infinitely prime solutions $p$ , where $∣∣.∣∣$ denotes the dis…

math.NT2024

Diophantine approximation with prime denominator in quadratic number fields under GRH

Stephan Baier, Sourav Das, Esrafil Ali Molla

MatomÃ¤ki proved that if $I^\pm \in R$ is irrational, then there are infinitely many primes $p$ such that $∣ I^\pm - a / p ∣ \leq p^{- 4/3 + ε}$ for a suitable integer a. In this…

math.NT2018

Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals

Stephan Baier, Vijay M. Patankar

Let $E$ be an elliptic curve over $Q$ . Let $p$ be a prime of good reduction for $E$ . Then, for a prime $p \neq = ℓ$ , the Frobenius automorphism associated to $p$ (unique…

math.NT2006

Bombieri-Vinogradov Type Theorem for Sparse Sets of Moduli

Stephan Baier, Liangyi Zhao

In this paper, we establish theorems of Bombieri-Vinogradov type and Barban-Davenport-Halberstam type for sparse sets of moduli. As an application, we prove that there exist infini…

math.NT2005

Addendum to "On the $p^{I^} »$ problem"

Stephan Baier

We prove that the conditions $I^» < 5/19$ and $L \leq T^{1/2}$ in Theorems 3 and 4 of our recent paper "On the $p^{I^} »$ problem" can be omitted.

cs.LG2017

Attention-based Information Fusion using Multi-Encoder-Decoder Recurrent Neural Networks

Stephan Baier, Sigurd Spieckermann, Volker Tresp

With the rising number of interconnected devices and sensors, modeling distributed sensor networks is of increasing interest. Recurrent neural networks (RNN) are considered particu…

math.NT2022

Asymptotic behavior of small solutions of quadratic congruences in three variables modulo prime powers

Stephan Baier, Anup Haldar

Let $p > 5$ be a fixed prime and assume that $I^\pm_{1}, I^\pm_{2}, I^\pm_{3}$ are coprime to $p$ . We study the asymptotic behavior of small solutions of congruences of the form $Î±_1x_1^2+Î±_2x_2^2+…

math.NT2008

On Primes in Quadratic Progressions

Stephan Baier, Liangyi Zhao

We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the au…

math.NT2022

A Bombieri-Vinogradov-type theorem with prime power moduli

Stephan Baier, Sudhir Pujahari

In 2020, Roger Baker \cite{Bak} proved a result on the exceptional set of moduli in the prime number theorem for arithmetic progressions of the following kind. Let $S$ be…

math.NT2024

A Bombieri-Vinogradov-type theorem for moduli with small radical

Stephan Baier, Sudhir Pujahari

In this article, we extend our recent work on a Bombieri-Vinogradov-type theorem for sparse sets of prime powers $p^{N} \leq x^{1/4 - ε}$ with $p \leq (lo g x)^{C}$ to sparse sets…

math.NT2026

A lower bound for classical Kloosterman sums and an application

Stephan Baier, Jishu Das, Jewel Mahajan

We present a lower bound for the classical Kloosterman sum $S (a, b; c)$ where $(ab, c) = 1$ and $c$ is an odd integer. We apply this lower bound for Kloosterman sums to derive an explic…

math.NT2019

Divisibility problems for function fields

Stephan Baier, Arpit Bansal, Rajneesh Kumar Singh

We investigate three combinatorial problems considered by ErdÃ¶s, Rivat, SarkÃ¶zy and SchÃ¶n regarding divisibility properties of sum sets and sets of shifted products of integers…

math.NT2015

Elliptic curves with square-free $I^$

Stephan Baier

Under the Riemann Hypothesis for Dirichlet L-functions, we improve on the error term in a smoothed version of an estimate for the density of elliptic curves with square-free $Î=D/…

math.NT2026

Character sums to prime power moduli evaluated at binary quadratic forms

Stephan Baier, Aishik Chattopadhyay

We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms. This complements estimates established by Heath-Brown for such character…

cs.LG2015

Predicting the Co-Evolution of Event and Knowledge Graphs

CristÃ³bal Esteban, Volker Tresp, Yinchong Yang +2

Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a…

math.NT2025

Small Solutions of generic ternary quadratic congruences

Stephan Baier, Aishik Chattopadhyay

We consider small solutions of quadratic congruences of the form $x_{1}^{2} + I^\pm_{2} x_{2}^{2} + I^\pm_{3} x_{3}^{2} \equiv 0 mod q$ , where $q = p^{m}$ is an odd prime power. Here, $I^\pm_{2}$ is arbitrary but fi…

math.NT2026

On bilinear sums with modular square roots and applications III

Stephan Baier

We continue our investigations of bilinear sums with modular square roots and the large sieve for square moduli in our recent article "On bilinear sums with modular square roots an…

math.NT2016

The large sieve with square norm moduli in Z[i]

Stephan Baier

We prove a large sieve inequality for square norm moduli in Z[i].

math.NT2013

Diophantine approximation on lines with prime constraints

Stephan Baier, Anish Ghosh

We study the problem of Diophantine approximation on lines in R^2 with prime numerator and denominator.

math.NT2024

Small solutions of generic ternary quadratic congruences to general moduli

Stephan Baier, Aishik Chattopadhyay

We study small non-trivial solutions of quadratic congruences of the form $x_{1}^{2} + I^\pm_{2} x_{2}^{2} + I^\pm_{3} x_{3}^{2} \equiv 0 mod q$ , with $q$ being an odd natural number, in an average sense. T…

math.NT2016

Diophantine approximation on lines in $C^{2}$ with Gaussian prime constraints

Stephan Baier

We study the problem of Diophantine approximation on lines in $C^{2}$ with numerators and denominators restricted to Gaussian primes.

math.NT2018

Moments of the error term in the Sato-Tate law for elliptic curves

Stephan Baier, Neha Prabhu

We derive new bounds for moments of the error in the Sato-Tate law over families of elliptic curves. Our estimates are stronger than those obtained by W.D. Banks and I.E. Shparlins…

math.NT2021

The large sieve for square moduli in function fields

Stephan Baier, Rajneesh Kumar Singh

We prove a lower and an upper bound for the large sieve with square moduli for function fields. These bounds correspond to bounds for the classical large sieve with square moduli e…

math.NT2007

Primes in Quadratic Progressions on Average

Stephan Baier, Liangyi Zhao

In this paper, we establish a theorem on the distribution of primes in quadratic progressions on average.

math.NT2022

Quantitative Oppenheim Conjecture for Quadratic Forms in 5 Variables over Function Fields

Stephan Baier, Arkaprava Bhandari

We translate Davenport's and Heilbronn's work on a quantitative version of the Oppenheim conjecture for indefinite diagonal quadratic forms in 5 variables into the setting of funct…

math.NT2021

Diophantine Approximation with Prime Restriction in Real Quadratic Number Fields

Stephan Baier, Dwaipayan Mazumder

The distribution of $I^\pm p$ modulo one, where $p$ runs over the rational primes and $I^\pm$ is a fixed irrational real, has received a lot of attention. It is natural to ask for which e…

math.NT2026

Diophantine approximation with sums of two squares

Stephan Baier, Habibur Rahaman

For any given positive definite binary quadratic form $Q$ with integer coefficients, we establish two results on Diophantine approximation with integers represented by $Q$ . Firstly…

math.NT2019

Large sieve inequality with power moduli for function fields

Stephan Baier, Rajneesh Kumar Singh

In this paper, we establish a general version of the large sieve with additive characters for restricted sets of moduli in arbitrary dimension for function fields. From this, we de…

math.NT2019

Central limit theorems for elliptic curves and modular forms with smooth weight functions

Stephan Baier, Neha Prabhu, Kaneenika Sinha

The second and third-named authors (arXiv:1705.04115) established a Central Limit Theorem for the error term in the Sato-Tate law for families of modular forms. This method was ada…

Publications (90)

Tensor Decompositions for Modeling Inverse Dynamics

The square sieve and the large sieve with square moduli

Quadratic congruences on average and rational points on cubic surfaces

Learning with Memory Embeddings

Improving Visual Relationship Detection using Semantic Modeling of Scene Descriptions

Mean values with cubic characters

Variance of primes in short residue classes for function fields

Large Sieve Inequalities for Characters to Powerful Moduli

A Remark on the Conjectures of Lang-Trotter and Sato-Tate on Average

The Sato-Tate Conjecture on Average for Small Angles

Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced version

Dimensions of Ext-groups of Weyl modules for GL_2

Diophantine approximation with primes from short intervals

Diophantine approximation with prime restriction in function fields

On the large sieve with square moduli

The large sieve with sparse sets of moduli

A Lower Bound for the Large Sieve with Square Moduli

The Lang-Trotter Conjecture on Average

The large sieve with power moduli for Z[i]

An uncountable subring of R with Hausdorff dimension zero

On Primes Represented by Quadratic Polynomials

On the large sieve with sparse sets of moduli

A Bombieri-Vinogradov theorem for sectors in real quadratic number fields

Multiple exponential sums and their applications to quadratic congruences

Improving Information Extraction from Images with Learned Semantic Models

On the Low-lying zeros of Hasse-Weil L-functions for Elliptic Curves

Conformance checking: A state-of-the-art literature review

Solutions of x12​+x22​−x32​=n2 with small x3​

Solving p-adic polynomial equations using Jarratt's Method

Large sieve inequalities with power moduli and Waring's problem

Large sieve with sparse sets of moduli for Z[i]

Multiplicative inverses in short intervals

Upper bounds for shifted moments of Dirichlet L-functions to a fixed modulus over function fields

On certain bilinear sums with modular square roots and applications

A note on Diophantine approximation with Gaussian primes

Exponential sums with Dirichlet coefficients of L-functions

Small Pythagorean triples modulo prime powers

On Hecke Eigenvalues at Piatetski-Shapiro Primes

On bilinear sums with modular square roots and applications II

Analyzing Customer Feedback for Product Fit Prediction

Small solutions to inhomogeneous and homogeneous quadratic congruences modulo prime powers

A note on the gaps between zeros of Epstein's zeta-functions on the critical line

A Subconvexity Bound for Automorphic L-functions for SL(3,Z)

A note on the distribution of prime ideals in real quadratic fields

The large sieve for square moduli, revisited

On the pI^» problem

Automorphisms with exotic orbit growth

Restricted simultaneous Diophantine approximation

Diophantine approximation with sums of two squares II

Prime powers dividing products of consecutive integer values of x2n+1

A refined version of the Lang-Trotter Conjecture

The large sieve inequality with square moduli for quadratic extensions of function fields

Type-Constrained Representation Learning in Knowledge Graphs

On the distribution of I^±p modulo one in imaginary quadratic number fields with class number one

On Hecke eigenvalues at primes of the form [g(n)]

On the distribution of I^±p modulo one in quadratic number fields

Exponential sums with coefficients of certain Dirichlet series

Partial progress towards the large sieve for square moduli

A Polya-Vinogradov-type inequality on Z[i]

Small solutions of ternary quadratic congruences with averaging over the moduli

Diophantine Approximation with Piatetski-Shapiro Primes

Diophantine approximation with prime denominator in real quadratic function fields

Diophantine approximation with prime denominator in quadratic number fields under GRH

Applications of the square sieve to a conjecture of Lang and Trotter for a pair of elliptic curves over the rationals

Bombieri-Vinogradov Type Theorem for Sparse Sets of Moduli

Addendum to "On the pI^» problem"

Attention-based Information Fusion using Multi-Encoder-Decoder Recurrent Neural Networks

Asymptotic behavior of small solutions of quadratic congruences in three variables modulo prime powers

On Primes in Quadratic Progressions

A Bombieri-Vinogradov-type theorem with prime power moduli

A Bombieri-Vinogradov-type theorem for moduli with small radical

A lower bound for classical Kloosterman sums and an application

Divisibility problems for function fields

Elliptic curves with square-free I^

Character sums to prime power moduli evaluated at binary quadratic forms

Predicting the Co-Evolution of Event and Knowledge Graphs

Small Solutions of generic ternary quadratic congruences

On bilinear sums with modular square roots and applications III

The large sieve with square norm moduli in Z[i]

The large sieve with power moduli for $Z [i]$

An uncountable subring of $R$ with Hausdorff dimension zero

Solutions of $x_{1}^{2} + x_{2}^{2} - x_{3}^{2} = n^{2}$ with small $x_{3}$

Solving $p$ -adic polynomial equations using Jarratt's Method

Large sieve with sparse sets of moduli for $Z [i]$

Upper bounds for shifted moments of Dirichlet $L$ -functions to a fixed modulus over function fields

A Subconvexity Bound for Automorphic $L$ -functions for $S L (3, Z)$

On the $p^{I^} »$ problem

Prime powers dividing products of consecutive integer values of $x^{2^{n}} + 1$

On the distribution of $I^\pm p$ modulo one in imaginary quadratic number fields with class number one

On Hecke eigenvalues at primes of the form $[g (n)]$

On the distribution of $I^\pm p$ modulo one in quadratic number fields

A Polya-Vinogradov-type inequality on $Z [i]$

Addendum to "On the $p^{I^} »$ problem"

Elliptic curves with square-free $I^$

Diophantine approximation on lines in $C^{2}$ with Gaussian prime constraints