4 citations · 4 across the 26 of their papers we have counts for
11 papers · 1 filter
Bounds for Moments of Twisted Fourier coefficients of Modular Forms
Peng Gao, Liangyi Zhao
We establish upper bounds for shifted moments of modular -functions to a fixed modulus as well as quadratic twists of modular -functions under the generalized Riemann hypothe…
Lower bounds for negative moments of Dirichlet -functions to a fixed modulus
Peng Gao
We establish lower bounds for the -th moment of central values of the family of primitive Dirichlet -functions to a fixed prime modulus for all real , assuming the non-…
Lower bounds for shifted moments of Dirichlet -functions of fixed modulus
Peng Gao, Liangyi Zhao
We establish sharp lower bounds for shifted (with two shifts) moments of Dirichlet -function of fixed modulus under the generalized Riemann hypothesis.
Upper bounds for shifted moments of quadratic Dirichlet -functions over function fields
Peng Gao, Liangyi Zhao
We establish sharp upper bounds on shifted moments of quadratic Dirichlet -functions over function fields. As an application, we prove some bounds for moments of quadratic Diric…
Upper bounds for shifted moments of Dirichlet -functions to a fixed modulus over function fields
Stephan Baier, Peng Gao
In this paper, we establish sharp upper bounds on shifted moments of the family of Dirichlet -functions to a fixed modulus over function fields. We apply the result to obtain up…
Shifted moments of quadratic Dirichlet -functions
Peng Gao, Liangyi Zhao
We establish sharp upper bounds for shifted moments of quadratic Dirichlet -function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moment…
Upper bounds for moments of zeta sums
Peng Gao
We establish upper bounds for moments of zeta sums using results on shifted moments of the Riemann zeta function under the Riemann hypothesis.
Twisted first moment of central values of primitive quadratic Dirichlet -functions
Peng Gao, Liangyi Zhao
We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet -functions using the method of double Dirichlet series together with a recu…
Bounds for moments of quadratic Dirichlet character sums
Peng Gao, Liangyi Zhao
We establish upper bounds for moments of smoothed quadratic Dirichlet character sums under the generalized Riemann hypothesis, confirming a conjecture of M. Jutila.
Ratios conjecture of quadratic Hecke -functions of prime-related moduli
Peng Gao, Liangyi Zhao
Using the method of multiple Dirichlet series, we develop L-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for quadratic familie…
Ratios conjecture of quartic -functions of prime moduli
Peng Gao, Liangyi Zhao
We apply the method of multiple Dirichlet series to develop -functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for the family of…