Zobrazeno 1 - 10
of 5 181
pro vyhledávání: '"Dirichlet L-functions"'
Autor:
Best, Christopher G.
We compute an asymptotic formula for the mixed second moment of the $\mu$-th and $\nu$-th derivatives of quadratic Dirichlet $L$-functions over monic, irreducible polynomials in the function field setting.
Comment: 12 pages, comments welcome
Comment: 12 pages, comments welcome
Externí odkaz:
http://arxiv.org/abs/2412.01462
Autor:
Gao, Peng
We establish lower bounds for the $2k$-th moment of central values of the family of primitive Dirichlet $L$-functions to a fixed prime modulus for all real $k<0$, assuming the non-vanishing of these $L$-values.
Comment: 6 pages
Comment: 6 pages
Externí odkaz:
http://arxiv.org/abs/2412.02080
Assuming the Generalized Riemann Hypothesis and a pair correlation conjecture for the zeros of Dirichlet $L$-functions, we establish the truth of a conjecture of Montgomery (in its corrected form stated by Friedlander and Granville) on the magnitude
Externí odkaz:
http://arxiv.org/abs/2411.19762
Assuming the existence of a Landau-Siegel zero, we establish an explicit Deuring-Heilbronn zero repulsion phenomenon for Dirichlet $L$-functions modulo $q$. Our estimate is uniform in the entire critical strip, and improves over the previous best kno
Externí odkaz:
http://arxiv.org/abs/2410.06082
Autor:
Leung, Sun-Kai
Given a large smooth conductor, we establish the nonvanishing of the central values for at least $35.9\%$ of the primitive Dirichlet $L$-functions.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/2410.01713
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:
Banks, William D.
For a primitive Dirichlet character $X$, a new hypothesis $RH_{sim}^\dagger[X]$ is introduced, which asserts that (1) all simple zeros of $L(s,X)$ in the critical strip are located on the critical line, and (2) these zeros satisfy some specific condi
Externí odkaz:
http://arxiv.org/abs/2410.11605
In 1970, Huxley obtained a sharp upper bound for the sixth moment of Dirichlet $L$-functions at the central point, averaged over primitive characters $\chi$ modulo $q$ and all moduli $q \leq Q$. In 2007, as an application of their ``asymptotic large
Externí odkaz:
http://arxiv.org/abs/2409.01457
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