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arXiv · 2108.01540

On the new identities of Dirichlet $L$-functions

Rong Ma·Jinglei Zhang·Yulong Zhang
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Abstract

Let $q\ge3$ be an integer, $\chi$ be a Dirichlet character modulo $q$, and $L(s,\chi)$ denote the Dirichlet $L$-functions corresponding to $\chi$. In this paper, we show some special function series, and give some new identities for the Dirichlet $L$-functions involving Gauss sums. Specially, we give specific identities for $L(2,\chi)$.

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Rong Ma, Jinglei Zhang, Yulong Zhang. 2021-08-03. On the new identities of Dirichlet $L$-functions. https://arxiv.org/abs/2108.01540

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