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arXiv · 1802.03896

Weighted first moments of some special quadratic Dirichlet $L$-functions

Peng Gao·Liangyi Zhao
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Abstract

In this paper, we obtain asymptotic formulas for weighted first moments of central values of families of primitive quadratic Dirichlet $L$-functions whose conductors comprise only primes that split in a given quadratic number field. We then deduce a non-vanishing result of these $L$-functions at the point $s=1/2$.

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Peng Gao, Liangyi Zhao. 2018-02-12. Weighted first moments of some special quadratic Dirichlet $L$-functions. https://arxiv.org/abs/1802.03896

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