4 citations · 4 across the 26 of their papers we have counts for
8 papers · 1 filter
First Moment of Quadratic Hecke -Functions with Lower Order Term
Peng Gao, Liangyi Zhao
We evaluate the first moment of the family of primitive quadratic Hecke -functions in the Gaussian field using the method of double Dirichlet series under the Riemann hypothesis…
Lower Bounds on High Moments of Twisted Fourier coefficients of Modular Forms
Peng Gao, Liangyi Zhao
For any large prime , and any real , we prove a lower bound for the following -th moment \begin{equation*} \sum_{\substack{χ\in X_q^*}} \Big| \sum_{n\leq…
The mollified fourth moment of Dirichlet -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 -functions to modulus mollified by a Dirichlet polynomial of l…
Shifted moments of cubic and quartic Dirichlet -functions
Peng Gao, Liangyi Zhao
We establish upper bounds for shifted moments of cubic and quartic Dirichlet -functions under the generalized Riemann hypothesis. As an application, we prove bounds for moments…
Twisted fourth moment of Dirichlet -functions to a fixed modulus
Peng Gao, Liangyi Zhao
We evaluate the twisted four moment on the critical line of the family of Dirichlet -functions to a fixed prime power modulus, obtaining an asymptotic formula with a power savin…
Bounds for Moments of Dirichlet -functions of fixed modulus on the critical line
Peng Gao, Liangyi Zhao
We study the -th moment of the family of Dirichlet -functions to a fixed prime modulus on the critical line and establish sharp lower bounds for all real and shar…
Twisted second moment of modular -functions to a fixed modulus
Peng Gao, Liangyi Zhao
We study asymptotically the twisted second moment of the family of modular -functions to a fixed modulus. As an application, we establish sharp lower bounds for all real $k \geq…
Upper bounds for moments of Dirichlet -functions to a fixed modulus
Peng Gao, Liangyi Zhao
We study the -th moment of central values of the family of Dirichlet -functions to a fixed prime modulus and establish sharp upper bounds for all real .