Year: 2021
Type: preprint
Abstract: In this paper we define a symmetric zeta function. We show that it can be analytically continued to a meromorphic function on $\mathbb{C}^3$ with only simple poles at some special hyperplanes. We also calculate the value of a multiple residue at one special point. For a divergent multiple series, which can be viewed as the value of the symmetric zeta function at the point $(1,1,1)$, we give a very detailed analysis on its growth and we relate it to the classical Euler constant.
Source: arXiv (Cornell University)
Author: Li, Jiangtao
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3207601446