Xiaosheng Wu

activity

20102025

most citedOn gaps between zeros of the Riemann zeta function

2 citations · 5 across the 18 of their papers we have counts for

collaborators

19 papers

math.NT2025

Mixed moments of twisted $L$ -functions

Zhenpeng Tang, Xiaosheng Wu

We establish an asymptotic formula with a power-saving error term for the twisted mixed moment of Dirichlet $L$ -functions and automorphic $L$ -functions twisted by all primitive cha…

math.NT2025

Upper Bounds for low moments of twisted Fourier coefficients of modular forms

Peng Gao, Xiaosheng Wu

For any large prime $q$ , $1 \leq x \leq q$ and any real $0 \leq k \leq 1$ , we prove an upper bound for the following $2 k$ -th moment $$\displaystyle \sum_{\substack{χ\bmod q}} \Big|…

math.NT2025

Bilinear forms with Kloosterman sums and moments of twisted L-functions

Djordje Milićević, Xinhua Qin, Xiaosheng Wu

We establish power-saving estimates for general bilinear forms with Kloosterman sums modulo arbitrary q, including when both variables are shorter than the Polya-Vinogradov range.…

math.NT2025

The mollified fourth moment of Dirichlet $L$ -functions

Peng Gao, Xiaosheng Wu, Liangyi Zhao

We prove an asymptotic formula with a power saving error term for the fourth moment of the family of Dirichlet $L$ -functions to modulus $q$ mollified by a Dirichlet polynomial of l…

math.NT2025

Non-vanishing of Dirichlet $L$ -functions at the Central Point

Xinhua Qin, Xiaosheng Wu

We prove that for at least $\frac{7}{19}$ of the primitive Dirichlet characters $χ$ with large general modulus, the central value $L (\frac{1}{2}, χ)$ is non-vanishing.

math.NT2023

Binomial pmf among arithmetic progressions and sieved sets in random walks

Jun Hong, Xiaosheng Wu, Shixin Zhu

We consider the distribution of the binomial probability mass function (pmf) among arithmetic progressions and obtain an average-type theorem. As applications, we consider the poss…

math.NT2023★ 1 cited

On the set of Kronecker numbers

Sayan Goswami, Wen Huang, XiaoSheng Wu

An positive even number is said to be a Kronecker number if it can be written in infinitely many ways as the difference between two primes, and it is believed that all even numbers…

math.NT2022

Bounds on bilinear forms with Kloosterman sums

Bryce Kerr, Igor E. Shparlinski, Xiaosheng Wu +1

We prove new bounds on bilinear forms with Kloosterman sums, complementing and improving a series of results by É. Fouvry, E. Kowalski and Ph. Michel (2014), V. Blomer, É. Fouvry,…

math.NT2021

Bounds for moments of modular $L$ -functions to a fixed modulus

Peng Gao, Xiaoguang He, Xiaosheng Wu

We study the $2 k$ -th moment of the family of twisted modular $L$ -functions to a fixed prime power modulus at the central values. We establish sharp lower bounds for all real $k \ge…

math.NT2020★ 1 cited

The fourth moment of Dirichlet $L$ -functions at the central value

Xiaosheng Wu

The asymptotic formula of the fourth moment of Dirichlet $L$ -functions at the central value was predicted in a conjecture by J. B. Conrey, D. W. Farmer, J. P. Keating, M. O. Rubins…

math.NT2020

The fourth moment of Dirichlet L-functions along the critical line

Xiaosheng Wu

For a positive integer $q \neq \equiv 2 (mod 4)$ , this work considers the fourth moment of Dirichlet $L$ -functions averaged over both $t \in [0, T]$ and primitive characters to modulus…

math.NT2018

The twisted mean square and critical zeros of Dirichlet $L$ -functions

Xiaosheng Wu

In this work, we obtain an asymptotic formula for the twisted mean square of a Dirichlet $L$ -function with a longer mollifier, whose coefficients are also more general than before.…

math.NT2017

The $k$ -tuple Prime Difference Champion

Libo Wu, Xiaosheng Wu

Let $D_{k}$ be a set with $k$ distinct elements of integers such that $d_{1} < d_{2} < \dots < d_{k}$ . We say $D_{k}^{*}$ is a $k$ -tuple prime difference champion ( $k$ -tuple PDC) for pr…

math.NT2015

On the set of the difference of primes

Wen Huang, XiaoSheng Wu

In this work we prove that the set of the difference of primes is a $Δ_{r}^{*}$ -set. The work is based on the recent dramatic new developments in the study of bounded gaps between prim…

math.NT2012

Distinct zeros of the Riemann zeta-functions

Wu Xiaosheng

In this paper, we prove that there are more than 66.036% of zeros of the Riemann zeta-function are distinct.

math.NT2012★ 1 cited

Distinct zeros and simple zeros of Dirichlet $L$ -functions

Wu Xiaosheng

In this paper, we study the number of additional zeros of Dirichlet $L$ -function caused by multiplicity by using Asymptotic Large Sieve. Then in asymptotic terms we prove that ther…

math.NT2011

On large gaps between zeros of the Riemann zeta-function

Feng Shaoji, Wu Xiaosheng

Assuming the Generalized Riemann Hypothesis(GRH), we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at least 3.072 times the averag…

math.NT2011

The $k$ -Tuple Jumping Champions among Consecutive Primes

Wu Xiaosheng, Feng Shaoji

For any real $x$ and any integer $k \geq 1$ , we say that a set $D_{k}$ of $k$ distinct integers is a $k$ -tuple jumping champion if it is the most common differences that occ…

math.NT2010★ 2 cited

On gaps between zeros of the Riemann zeta function

Shaoji Feng, Xiaosheng Wu

Assuming the Riemann Hypothesis, we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at least 2.7327 times the average spacing and in…

Mixed moments of twisted L-functions

Upper Bounds for low moments of twisted Fourier coefficients of modular forms

Bilinear forms with Kloosterman sums and moments of twisted L-functions

The mollified fourth moment of Dirichlet L-functions

Non-vanishing of Dirichlet L-functions at the Central Point

Binomial pmf among arithmetic progressions and sieved sets in random walks

On the set of Kronecker numbers

Bounds on bilinear forms with Kloosterman sums

Bounds for moments of modular L-functions to a fixed modulus

The fourth moment of Dirichlet L-functions at the central value

The fourth moment of Dirichlet L-functions along the critical line

The twisted mean square and critical zeros of Dirichlet L-functions

The k-tuple Prime Difference Champion

On the set of the difference of primes

Distinct zeros of the Riemann zeta-functions

Distinct zeros and simple zeros of Dirichlet L-functions

On large gaps between zeros of the Riemann zeta-function

The k-Tuple Jumping Champions among Consecutive Primes

On gaps between zeros of the Riemann zeta function

Mixed moments of twisted $L$ -functions

The mollified fourth moment of Dirichlet $L$ -functions

Non-vanishing of Dirichlet $L$ -functions at the Central Point

Bounds for moments of modular $L$ -functions to a fixed modulus

The fourth moment of Dirichlet $L$ -functions at the central value

The twisted mean square and critical zeros of Dirichlet $L$ -functions

The $k$ -tuple Prime Difference Champion

Distinct zeros and simple zeros of Dirichlet $L$ -functions

The $k$ -Tuple Jumping Champions among Consecutive Primes