Zobrazeno 1 - 10
of 289
pro vyhledávání: '"Zhao, Liangyi"'
Autor:
Gao, Peng, Zhao, Liangyi
We establish sharp lower bounds for shifted moments of Dirichlet $L$-function of fixed modulus under the generalized Riemann hypothesis.
Externí odkaz:
http://arxiv.org/abs/2411.03692
Autor:
Gao, Peng, Zhao, Liangyi
We establish sharp upper bounds on shifted moments of quadratic Dirichlet $L$-functions over function fields. As an application, we prove some bounds for moments of quadratic Dirichlet character sums over function fields.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2408.02880
Autor:
Gao, Peng, Zhao, Liangyi
We establish sharp upper bounds for shifted moments of quadratic Dirichlet $L$-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
http://arxiv.org/abs/2406.18024
Autor:
Gao, Peng, Zhao, Liangyi
We evaluate the twisted first moment of central values of the family of primitive quadratic Dirichlet $L$-functions using the method of double Dirichlet series together with a recursive argument. Our main result is an asymptotic formula with an error
Externí odkaz:
http://arxiv.org/abs/2405.15980
Autor:
Gao, Peng, Zhao, Liangyi
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 families of Dirichlet and Hecke L-functions of primerelated moduli of imagina
Externí odkaz:
http://arxiv.org/abs/2404.05081
Autor:
Gao, Peng, Zhao, Liangyi
We apply the method of multiple Dirichlet series to develop $L$-functions ratios conjecture with one shift in both the numerator and denominator in certain ranges for the family of quartic Hecke $L$-functions of prime moduli over the Gaussian field u
Externí odkaz:
http://arxiv.org/abs/2402.17198
Autor:
Gao, Peng, Zhao, Liangyi
We establish upper bounds for moments of smoothed quadratic Dirichlet character sums under the generalized Riemann hypothesis, confirming a conjecture of M. Jutila.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2403.14634
Autor:
Gao, Peng, Zhao, Liangyi
We develop $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke $L$-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the generalized R
Externí odkaz:
http://arxiv.org/abs/2311.08626
Autor:
Gao, Peng, Zhao, Liangyi
We develop the ratios conjecture with one shift in the numerator and denominator in certain ranges for families of primitive quadratic Hecke $L$-functions of imaginary quadratic number fields with class number one using multiple Dirichlet series unde
Externí odkaz:
http://arxiv.org/abs/2309.13811
First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters
Autor:
Gao, Peng, Zhao, Liangyi
Publikováno v:
J. Number Theory, vol. 261, 2024, pp. 125--142
We evaluate asymptotically the smoothed first moment of central values of families of primitive cubic, quartic and sextic Dirichlet $L$-functions, using the method of double Dirichlet series. Quantitative non-vanishing result for these $L$-values are
Externí odkaz:
http://arxiv.org/abs/2308.10602