Xiaosheng Wu

collaborators

5 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{Ï\bmod q}} \Big…

math.NT2025

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

Djordje MiliÄeviÄ, 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 $I ¨ $ with large general modulus, the central value $L (\frac{1}{2}, I ¨ )$ is non-vanishing.

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

Mixed moments of twisted $L$ -functions

The mollified fourth moment of Dirichlet $L$ -functions

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