9 papers
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…
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 .