Further Insights into the Mysteries of the Values of Zeta Functions at Integers-Reference-Cited by-同舟云学术

Further Insights into the Mysteries of the Values of Zeta Functions at Integers

Published:2023-08-01 Issue:4 Volume:73 Page:887-910
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Mináč Ján¹,Nguyen Tung T.²,Tân Nguyễn Duy³

Affiliation:

1. * Department of Mathematics, Western University , London , Ontario , CANADA

2. ** Brain and Mind Institute and Department of Mathematics, Western University , London , Ontario , CANADA

3. *** School of Applied Mathematics and Informatics, Hanoi University of Science and Technology , 01 Dai Co Viet Road , Hanoi , VIETNAM

Abstract

ABSTRACTWe present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely, we are able to relate these values to areas related to partial sums of powers. We apply these results to further interpretations of values ofL-functions at negative integers. We hint in a very brief way at some expected connections of this work with other current efforts to understand the mysteries of the values of zeta functions at integers.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2023-0066/pdf

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