Xiannan Li

activity

20092026

most citedUpper bounds on L-functions at the edge of the critical strip

18 citations · 35 across the 19 of their papers we have counts for

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22 papers · 1 filter

math.NT2026

Simultaneous non-vanishing of twists of $GL_{3}$ and $GL_{1}$ $L$ -functions

Junxian Li, Xiannan Li, Yongxiao Lin

We show that for a fixed $SL_{3} (Z)$ Hecke--Maass cusp form $F$ , there are infinitely many primitive Dirichlet characters $χ$ such that $L (1/2, F \times χ)$ and $L(1/…

math.NT2026

One-level densities of large even and odd orthogonal families of automorphic L-functions

Vorrapan Chandee, Xiannan Li, Micah B. Milinovich

We prove one-level density results for L-functions attached to primitive forms of level q, averaged over square-free q, conditional on the Generalized Riemann Hypothesis (GRH). We…

math.NT2025

The $n^{t h}$ centered moments of a large orthogonal family of automorphic $L$ -functions

Vorrapan Chandee, Yoonbok Lee, Xiannan Li

We obtain the $n$ th centered moments of one level densities of a large orthogonal family of $L$ -functions associated with holomorphic Hecke newforms of level $q$ , averaged over $q\…

math.NT2024

The sixth moment of Dirichlet L-functions at the central point

Vorrapan Chandee, Xiannan Li, Kaisa Matomäki +1

In 1970, Huxley obtained a sharp upper bound for the sixth moment of Dirichlet $L$ -functions at the central point, averaged over primitive characters $χ$ modulo $q$ and all moduli…

math.NT2023

Low-lying zeros of a large orthogonal family of automorphic $L$ -functions

Siegfred Baluyot, Vorrapan Chandee, Xiannan Li

We study a new orthogonal family of $L$ -functions associated with holomorphic Hecke newforms of level $q$ , averaged over $q ≍ Q$ . To illustrate our methods, we prove a one lev…

math.NT2023

The eighth moment of Dirichlet L-functions II

Vorrapan Chandee, Xiannan Li, Kaisa Matomäki +1

We prove an asymptotic formula for the eighth moment of Dirichlet $L$ -functions averaged over primitive characters $χ$ modulo $q$ , over all moduli $q \leq Q$ and with a short averag…

math.NT2022★ 2 cited

Moments of quadratic twists of modular $L$ -functions

Xiannan Li

We prove an asymptotic for the second moment of quadratic twists of a modular $L$ -function. This was previously known conditionally on GRH by the work of Soundararajan and Young.

math.NT2022

On Benford's Law for multiplicative functions

Vorrapan Chandee, Xiannan Li, Paul Pollack +1

We provide a criterion to determine whether a real multiplicative function is a strong Benford sequence. The criterion implies that the $k$ -divisor functions, where $k \neq = 1 0^{j}$ ,…

math.NT2021

The second moment of $G L (4) \times G L (2)$ $L$ -functions at special points

Vorrapan Chandee, Xiannan Li

In this paper, we obtain upper bounds for the second moment of $L (u_{j} \times ϕ, \frac{1}{2} + i t_{j})$ , where $ϕ$ is a Hecke Maass form for $S L (4, Z)$ , and $u_{j}$ is taken fro…

math.NT2021

Prime values of a sparse polynomial sequence

Xiannan Li

A distinguishing feature of certain intractable problems in prime number theory is the sparsity of the underlying sequence. Motivated by the general problem of finding primes in sp…

math.NT2017

The eighth moment of the family of $Γ_{1} (q)$ -automorphic $L$ -functions

Vorrapan Chandee, Xiannan Li

We prove a Lindelöf on average bound for the eighth moment of a family of $L$ -functions attached to automorphic forms on $G L (2)$ , the first time this has been accomplished. Previou…

math.NT2017★ 10 cited

The sixth moment of automorphic $L$ -functions

Vorrapan Chandee, Xiannan Li

In this paper, we consider the $L$ -functions $L (s, f)$ where $f$ is an eigenform for the congruence subgroup $Γ_{1} (q)$ . We prove an asymptotic formula for the sixth moment of this f…

math.NT2016

A quadratic divisor problem and moments of the Riemann zeta-function

Sandro Bettin, H. M. Bui, Xiannan Li +1

We estimate asymptotically the fourth moment of the Riemann zeta-function twisted by a Dirichlet polynomial of length $T^{\frac{1}{4} - ε}$ . Our work relies crucially on Watt…

math.NT2015

Almost prime triples and Chen's Theorem

D. R. Heath-Brown, Xiannan Li

We show that there are infinitely many primes $p$ such that not only does $p + 2$ have at most two prime factors, but $p + 6$ also has a bounded number of prime divisors. This refi…

math.NT2015

Primes values of $a^{2} + p^{4}$

D. R. Heath-Brown, Xiannan Li

We prove an asymptotic formula for the number of primes of the shape $a^{2} + p^{4}$ , thereby refining the well known work of Friedlander and Iwaniec. Along the way, we prove a result o…

math.NT2013

Conditional bounds for the least quadratic non-residue and related problems

Youness Lamzouri, Xiannan Li, Kannan Soundararajan

This paper studies explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improv…

math.NT2012★ 3 cited

The Riemann-zeta function on vertical arithmetic progressions

Xiannan Li, Maksym Radziwill

We show that the twisted second moments of the Riemann zeta function averaged over the arithmetic progression $1/2 + i (an + b)$ with $a > 0$ , $b$ real, exhibits a remarkable corres…

math.NT2012

Additive twists of Fourier coefficients of GL(3) Maass forms

Xiannan Li

We prove cancellation in a sum of Fourier coefficents of a GL(3) form $F$ twisted by additive characters, uniformly in the form $F$ .

math.NT2012★ 1 cited

Lower bounds for small fractional moments of Dirichlet $L$ -functions

Vorrapan Chandee, Xiannan Li

We prove a lower bound of the correct order of magnitude in the conductor aspect for small rational moments of Drichlet $L$ -functions. Such bounds require new techniques, which is…

math.NT2010★ 1 cited

The smallest prime that does not split completely in a number field

Xiannan Li

We study the problem of bounding the least prime that does not split completely in a number field. This is a generalization of the classic problem of bounding the least quadratic n…

math.NT2009

The argument of the Riemann $Ξ$ -function off the critical line

Xiannan Li

We examine the behaviour of the zeros of the real and imaginary parts of $ξ (s)$ on the vertical line $ℜ s = 1/2 + λ$ , for $λ \neq = 0$ . This can be rephrased in terms of studying the…

math.NT2009★ 18 cited

Upper bounds on L-functions at the edge of the critical strip

Xiannan Li

The problem of finding upper bounds for L-functions at the edge of the critical strip has a long and interesting history. Here, the situation for classical L-functions such as Diri…

Simultaneous non-vanishing of twists of GL3​ and GL1​ L-functions

One-level densities of large even and odd orthogonal families of automorphic L-functions

The nth centered moments of a large orthogonal family of automorphic L-functions

The sixth moment of Dirichlet L-functions at the central point

Low-lying zeros of a large orthogonal family of automorphic L-functions

The eighth moment of Dirichlet L-functions II

Moments of quadratic twists of modular L-functions

On Benford's Law for multiplicative functions

The second moment of GL(4)×GL(2) L-functions at special points

Prime values of a sparse polynomial sequence

The eighth moment of the family of Γ1​(q)-automorphic L-functions

The sixth moment of automorphic L-functions

A quadratic divisor problem and moments of the Riemann zeta-function

Almost prime triples and Chen's Theorem

Primes values of a2+p4

Conditional bounds for the least quadratic non-residue and related problems

The Riemann-zeta function on vertical arithmetic progressions

Additive twists of Fourier coefficients of GL(3) Maass forms

Lower bounds for small fractional moments of Dirichlet L-functions

The smallest prime that does not split completely in a number field

The argument of the Riemann Ξ-function off the critical line

Upper bounds on L-functions at the edge of the critical strip

Simultaneous non-vanishing of twists of $GL_{3}$ and $GL_{1}$ $L$ -functions

The $n^{t h}$ centered moments of a large orthogonal family of automorphic $L$ -functions

Low-lying zeros of a large orthogonal family of automorphic $L$ -functions

Moments of quadratic twists of modular $L$ -functions

The second moment of $G L (4) \times G L (2)$ $L$ -functions at special points

The eighth moment of the family of $Γ_{1} (q)$ -automorphic $L$ -functions

The sixth moment of automorphic $L$ -functions

Primes values of $a^{2} + p^{4}$

Lower bounds for small fractional moments of Dirichlet $L$ -functions

The argument of the Riemann $Ξ$ -function off the critical line