Negative first moment of quadratic twists of $L$-functions

Peng Gao; Liangyi Zhao

doi:10.1016/j.jnt.2025.01.003

paper

Negative first moment of quadratic twists of $L$ -functions

arXiv:2303.05055 · doi:10.1016/j.jnt.2025.01.003

Abstract

We evaluate asymptotically the negative first moment at points larger than $1/2$ of the family of quadratic twists of automorphic $L$ -functions using multiple Dirichlet series under the generalized Riemann hypothesis and the Ramanujan-Petersson conjecture.

10 pages

References in corpus (2)

Singularity dominated strong fluctuations for some random matrix averages
Complex Moments and the distribution of Values of $L (1, χ_{D})$ over Function Fields with Applications to Class Numbers

Negative first moment of quadratic twists of L-functions

Abstract

References in corpus (2)

Negative first moment of quadratic twists of $L$ -functions