二次Dirichlet $L$-素数相关模函数矩的界

Pub Date : 2021-05-08 DOI:10.4064/cm8650-1-2022

Peng Gao, Liangyi Zhao

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引用次数: 4

摘要

．本文研究了模为8p的二次Dirichlet L -函数族中心值的k阶矩，其中p的取值范围为奇数素数。在广义黎曼假设成立的前提下，我们为所有实k≥0时这些L值的k次幂矩建立了清晰的上界和下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bounds for moments of quadratic Dirichlet $L$-functions of prime-related moduli

. In this paper, we study the k -th moment of central values of the family of quadratic Dirichlet L -functions of moduli 8 p , with p ranging over odd primes. Assuming the truth of the generalized Riemann hypothesis, we establish sharp upper and lower bounds for the k -th power moment of these L -values for all real k ≥ 0.

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