19 papers
Murmurations of quadratic Hecke -functions of the Gaussian field
Peng Gao, Liangyi Zhao
In this paper, we evaluate the murmuration density for the family of quadratic Hecke -functions of the Gaussian field under the generalized Riemann hypothesis.
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…
High moments of random multiplicative functions twisted by Fourier coefficients of modular forms
Peng Gao, Liangyi Zhao
Let denote the Fourier coefficients of a fixed modular form and a Steinhaus or Rademacher random multiplicative function. In this paper, we determine, under the gene…
Low moments of random multiplicative functions twisted by Fourier coefficients of modular forms
Peng Gao, Liangyi Zhao
Let denote the Fourier coefficients of a fixed modular form and a Steinhaus or Rademacher random multiplicative function. In this paper, we determine the order of ma…
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…
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…