B. Borda

activity

20162026

most citedMaximizing Sudler products via Ostrowski expansions and cotangent sums

7 citations · 28 across the 22 of their papers we have counts for

collaborators

28 papers

math.NT2026

Equidistribution of number theoretic point sets in the torus and the sphere in Wasserstein metric and $L^{2}$ discrepancy

Bence Borda, Filippo Giannoni

We find the exact rate of equidistribution of several arithmetic point configurations in Wasserstein metric and $L^{2}$ discrepancy with respect to balls. Kronecker sequences in the…

math.PR2025

Random walks and quadratic number fields

Bence Borda

We establish a novel type of connection between random walks and analytic number theory. Working with a random walk on the circle group $R / Z$ in which each step i…

math.CA2025

Smoothing inequalities for transport metrics in compact spaces

Bence Borda, Jean-Claude Cuenin

We prove general upper estimates for the distance between two Borel probability measures in Wasserstein metric in terms of the Fourier transforms of the measures. We work in compac…

math.PR2023

Eigenvalues of random matrices from compact classical groups in Wasserstein metric

Bence Borda

The circular unitary ensemble and its generalizations concern a random matrix from a compact classical group $U (N)$ , $SU (N)$ , $O (N)$ , $SO (N)$ or…

math.NT2023

Limit laws for cotangent and Diophantine sums

Bence Borda, Lorenz Frühwirth, Manuel Hauke

Limit laws for ergodic averages with a power singularity over circle rotations were first proved by Sinai and Ulcigrai, as well as Dolgopyat and Fayad. In this paper, we prove limi…

math.CA2023

Riesz Energy, $L^{2}$ Discrepancy, and Optimal Transport of Determinantal Point Processes on the Sphere and the Flat Torus

Bence Borda, Peter Grabner, Ryan W. Matzke

Determinantal point processes exhibit an inherent repulsive behavior, thus providing examples of very evenly distributed point sets on manifolds. In this paper, we study the so-cal…

math.NT2023★ 1 cited

Remarks on sums of reciprocals of fractional parts

Bence Borda

The Diophantine sums $\sum_{n = 1}^{N} ∥ n α ∥^{- 1}$ and $\sum_{n = 1}^{N} n^{- 1} ∥ n α ∥^{- 1}$ appear in many different areas including the ergodic theory of circle rotations, lattice p…

math.NT2023

Pointwise and correlation bounds on Dedekind sums over small subgroups

Bence Borda, Marc Munsch, Igor Shparlinski

We obtain new bounds, pointwisely and on average, for Dedekind sums $s (λ, p)$ modulo a prime $p$ with $λ$ of small multiplicative order $d$ modulo $p$ . Assuming the infinit…

math.DS2023★ 1 cited

Limit laws of maximal Birkhoff sums for circle rotations via quantum modular forms

Bence Borda

In this paper, we show how quantum modular forms naturally arise in the ergodic theory of circle rotations. Working with the classical Birkhoff sum $S_N(α)=\sum_{n=1}^N (\{ n α\}-1…

math.DS2023★ 3 cited

Equidistribution of continued fraction convergents in $SL (2, Z_{m})$ with an application to local discrepancy

Bence Borda

Consider the sequence of continued fraction convergents $p_{n} / q_{n}$ to a random irrational number. We study the distribution of the sequences $p_{n} (mod m)$ and $q_{n} (mod m)$ with a…

math.NT2022

On the distribution of partial quotients of reduced fractions with fixed denominator

Christoph Aistleitner, Bence Borda, Manuel Hauke

In this paper, we study distributional properties of the sequence of partial quotients in the continued fraction expansion of fractions $a / N$ , where $N$ is fixed and $a$ runs throu…

math.PR2022★ 3 cited

Random walks on the circle and Diophantine approximation

Istvan Berkes, Bence Borda

Random walks on the circle group $R / Z$ whose elementary steps are lattice variables with span $α \neq \in Q$ or $p / q \in Q$ taken mod $Z$ …

math.NT2022

On the metric theory of approximations by reduced fractions: a quantitative Koukoulopoulos-Maynard theorem

Christoph Aistleitner, Bence Borda, Manuel Hauke

Let $ψ : N \to [0, 1/2]$ be given. The Duffin-Schaeffer conjecture, recently resolved by Koukoulopoulos and Maynard, asserts that for almost all reals $α$ there are infinite…

math.NT2021

Optimal and typical $L^{2}$ discrepancy of 2-dimensional lattices

Bence Borda

We undertake a detailed study of the $L^{2}$ discrepancy of rational and irrational 2-dimensional lattices either with or without symmetrization. We give a full characterization of l…

math.NT2021★ 1 cited

A conjecture of Zagier and the value distribution of quantum modular forms

Christoph Aistleitner, Bence Borda

In his influential paper on quantum modular forms, Zagier developed a conjectural framework describing the behavior of certain quantum knot invariants under the action of the modul…

math.PR2021★ 5 cited

Empirical measures and random walks on compact spaces in the quadratic Wasserstein metric

Bence Borda

Estimating the rate of convergence of the empirical measure of an i.i.d. sample to the reference measure is a classical problem in probability theory. Extending recent results of A…

math.NT2021★ 7 cited

Maximizing Sudler products via Ostrowski expansions and cotangent sums

Christoph Aistleitner, Bence Borda

There is an extensive literature on the asymptotic order of Sudler's trigonometric product $P_{N} (α) = \prod_{n = 1}^{N} ∣2 sin (π n α) ∣$ for fixed or for "typical" values of $α$ . In th…

math.DS2021★ 1 cited

On the distribution of Sudler products and Birkhoff sums for the irrational rotation

Bence Borda

We study the value distribution of the Sudler product $\prod_{n = 1}^{N} ∣2 sin (π n α) ∣$ and the Diophantine product $\prod_{n = 1}^{N} (2 e ∥ n α ∥)$ for various irrational $α$ , as $N$ ra…

math.PR2020★ 2 cited

On the discrepancy of random subsequences of ${n α}$ II

Istvan Berkes, Bence Borda

Let $α$ be an irrational number, let $X_{1}, X_{2}, \dots$ be independent, identically distributed, integer-valued random variables, and put $S_{k} = \sum_{j = 1}^{k} X_{j}$ . Assuming that $X_1…

math.CA2020

Berry-Esseen smoothing inequality for the Wasserstein metric on compact Lie groups

Bence Borda

We prove a sharp general inequality estimating the distance of two probability measures on a compact Lie group in the Wasserstein metric in terms of their Fourier transforms. We us…

math.NT2020

Quantum invariants of hyperbolic knots and extreme values of trigonometric products

Christoph Aistleitner, Bence Borda

In this paper we study the relation between the function $J_{4_{1}, 0}$ , which arises from a quantum invariant of the figure-eight knot, and Sudler's trigonometric product. We find $J…

math.PR2020

Equidistribution of random walks on compact groups II. The Wasserstein metric

Bence Borda

We consider a random walk $S_{k}$ with i.i.d. steps on a compact group equipped with a bi-invariant metric. We prove quantitative ergodic theorems for the sum $\sum_{k = 1}^{N} f (S_{k})$ w…

math.NT2019★ 4 cited

On the discrepancy of random subsequences of ${n α}$

Istvan Berkes, Bence Borda

For irrational $α$ , ${n α}$ is uniformly distributed mod 1 in the Weyl sense, and the asymptotic behavior of its discrepancy is completely known. In contrast, very few precise res…

math.PR2019

Equidistribution of random walks on compact groups

Bence Borda

Let $X_{1}, X_{2}, \dots$ be independent, identically distributed random variables taking values from a compact metrizable group $G$ . We prove that the random walk $S_k=X_1 X_2 \cdots…

Equidistribution of number theoretic point sets in the torus and the sphere in Wasserstein metric and L2 discrepancy

Random walks and quadratic number fields

Smoothing inequalities for transport metrics in compact spaces

Eigenvalues of random matrices from compact classical groups in Wasserstein metric

Limit laws for cotangent and Diophantine sums

Riesz Energy, L2 Discrepancy, and Optimal Transport of Determinantal Point Processes on the Sphere and the Flat Torus

Remarks on sums of reciprocals of fractional parts

Pointwise and correlation bounds on Dedekind sums over small subgroups

Limit laws of maximal Birkhoff sums for circle rotations via quantum modular forms

Equidistribution of continued fraction convergents in SL(2,Zm​) with an application to local discrepancy

On the distribution of partial quotients of reduced fractions with fixed denominator

Random walks on the circle and Diophantine approximation

On the metric theory of approximations by reduced fractions: a quantitative Koukoulopoulos-Maynard theorem

Optimal and typical L2 discrepancy of 2-dimensional lattices

A conjecture of Zagier and the value distribution of quantum modular forms

Empirical measures and random walks on compact spaces in the quadratic Wasserstein metric

Maximizing Sudler products via Ostrowski expansions and cotangent sums

On the distribution of Sudler products and Birkhoff sums for the irrational rotation

On the discrepancy of random subsequences of {nα} II

Berry-Esseen smoothing inequality for the Wasserstein metric on compact Lie groups

Quantum invariants of hyperbolic knots and extreme values of trigonometric products

Equidistribution of random walks on compact groups II. The Wasserstein metric

On the discrepancy of random subsequences of {nα}

Equidistribution of random walks on compact groups

Equidistribution of number theoretic point sets in the torus and the sphere in Wasserstein metric and $L^{2}$ discrepancy

Riesz Energy, $L^{2}$ Discrepancy, and Optimal Transport of Determinantal Point Processes on the Sphere and the Flat Torus

Equidistribution of continued fraction convergents in $SL (2, Z_{m})$ with an application to local discrepancy

Optimal and typical $L^{2}$ discrepancy of 2-dimensional lattices

On the discrepancy of random subsequences of ${n α}$ II

On the discrepancy of random subsequences of ${n α}$