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arXiv · 2308.10602

First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters

Peng Gao·Liangyi Zhao
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Abstract

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 also proved.

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Peng Gao, Liangyi Zhao. 2023-08-21. First moment of central values of some primitive Dirichlet $L$-functions with fixed order characters. https://doi.org/10.1016/j.jnt.2024.02.007

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