39 citations · 227 across the 91 of their papers we have counts for
91 papers
On the Gauss circle problem over smooth numbers
Peng Gao
The Gauss circle problem concerns with the evaluation of , where denotes the number of representations of as sums of two squares and . Let…
Ratios conjecture for primitive quadratic Hecke -functions
Peng Gao, Liangyi Zhao
We develop the ratios conjecture with one shift in the numerator and denominator in certain ranges for families of primitive quadratic Hecke -functions of imaginary quadratic nu…
First moment of central values of some primitive Dirichlet -functions with fixed order characters
Peng Gao, Liangyi Zhao
We evaluate asymptotically the smoothed first moment of central values of families of primitive cubic, quartic and sextic Dirichlet -functions, using the method of double Dirich…
First moment of central values of Hecke -functions with Fixed Order Characters
Peng Gao, Liangyi Zhao
We evaluate asymptotically the smoothed first moment of central values of families of quadratic, cubic, quartic and sextic Hecke -functions over various imaginary quadratic numb…
Ratios conjecture for quadratic twist of modular -functions
Peng Gao, Liangyi Zhao
We develop the -functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of quadratic twist of modular -functions using mu…
First moment of central values of quadratic Dirichlet -functions
Peng Gao, Liangyi Zhao
We evaluate the first moment of central values of the family of quadratic Dirichlet -functions using the method of double Dirichlet series. Under the generalized Riemann hypothe…