虚二次域上值的显式恒等式

IF 1 3区 数学 Q3 MATHEMATICS, APPLIED
Soumyarup Banerjee , Rahul Kumar
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引用次数: 0

摘要

本文研究了虚二次域上Dedekind zeta函数的特殊值。在文献中,Dedekind zeta函数在任何全实数域上的任何偶数处的值都是众所周知的。本文给出了虚二次域上Dedekind zeta函数的偶值和奇值恒等式,类似于Ramanujan关于q上zeta的偶值和奇值恒等式,此外,虚二次域上的任何复zeta值也可以由我们的恒等式求出。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Explicit identities on zeta values over imaginary quadratic fields
In this article, we study special values of the Dedekind zeta function over an imaginary quadratic field. The values of the Dedekind zeta function at any even integer over any totally real number field are quite well known in literature. We here exhibit the identities for both even and odd values of the Dedekind zeta function over an imaginary quadratic field which are analogous to Ramanujan's identities for even and odd zeta values over Q. Moreover, any complex zeta values over imaginary quadratic field may also be evaluated from our identities.
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来源期刊
Advances in Applied Mathematics
Advances in Applied Mathematics 数学-应用数学
CiteScore
2.00
自引率
9.10%
发文量
88
审稿时长
85 days
期刊介绍: Interdisciplinary in its coverage, Advances in Applied Mathematics is dedicated to the publication of original and survey articles on rigorous methods and results in applied mathematics. The journal features articles on discrete mathematics, discrete probability theory, theoretical statistics, mathematical biology and bioinformatics, applied commutative algebra and algebraic geometry, convexity theory, experimental mathematics, theoretical computer science, and other areas. Emphasizing papers that represent a substantial mathematical advance in their field, the journal is an excellent source of current information for mathematicians, computer scientists, applied mathematicians, physicists, statisticians, and biologists. Over the past ten years, Advances in Applied Mathematics has published research papers written by many of the foremost mathematicians of our time.
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