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arXiv · 2303.05055

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

Peng Gao·Liangyi Zhao
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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.

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Peng Gao, Liangyi Zhao. 2023-03-09. Negative first moment of quadratic twists of $L$-functions. https://doi.org/10.1016/j.jnt.2025.01.003

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