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浙江大学学报(理学版)  2020, Vol. 47 Issue (4): 435-441    DOI: 10.3785/j.issn.1008-9497.2020.04.005
数学与计算机科学     
关于伯努利多项式和Dirichlet L-函数的均值问题
张艺雪
西北大学 数学学院, 陕西 西安 710127
On the Bernoulli polynomials and mean square value of the Dirichlet L-functions
ZHANG Yixue
School of Mathematics, Northwest University, Xi’an 710127, China
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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。
关键词: Dirichlet L-函数伯努利多项式卷积和基本方法等式分析方法    
Abstract: 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.
Key words: Dirichlet L-function    Bernoulli polynomials    elementary method    analytic methods    identity    convolution sums
收稿日期: 2019-04-04 出版日期: 2020-07-25
CLC:  O156.4  
基金资助: 国家自然科学基金资助项目(11771351,11826205).
作者简介: 张艺雪(1994—),ORCID:http://orcid.org/0000-0001-6738-8618,女,硕士研究生,主要从事解析数论研究,E-mail:zhangyixue@stumail.nwu.edu.cn.。
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张艺雪. 关于伯努利多项式和Dirichlet L-函数的均值问题[J]. 浙江大学学报(理学版), 2020, 47(4): 435-441.

ZHANG Yixue. On the Bernoulli polynomials and mean square value of the Dirichlet L-functions. Journal of Zhejiang University (Science Edition), 2020, 47(4): 435-441.

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https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2020.04.005        https://www.zjujournals.com/sci/CN/Y2020/V47/I4/435

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