关于伯努利多项式和Dirichlet L-函数的均值问题  

On the Bernoulli polynomials and mean square value of the Dirichlet L-functions

作　　者：张艺雪 ZHANG Yixue(School of Mathematics,Northwest University,Xi’an 710127,China)

机构地区：[1]西北大学数学学院,陕西西安710127

出　　处：《浙江大学学报（理学版）》2020年第4期435-441,共7页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11771351,11826205).

摘　　要：研究一类涉及伯努利多项式卷积和的计算问题,并利用初等方法证明了恒等式。作为对此恒等式的应用,得到了一系列与伯努利数相关的有趣等式。将这些等式进行推广,证明了2个与Dirichlet L-函数有关的简单结果。揭示了伯努利多项式与L-函数之间的关系。In this paper, we studied the computational problem of one kind convolution sums involving Bernoulli polynomials, and proved an identity by elementary methods. As some applications of this identity, we obtained a series of interesting identities related to Bernoulli numbers. As an exploration, we also obtained two simple results related to Dirichlet L-functions which profoundly revealed the close relationship between L-functions and Bernoulli polynomials.

关 键 词：Dirichlet L-函数 伯努利多项式 卷积和 基本方法 分析方法 等式 

分 类 号：O156.4[理学—数学]