Remark on a symmetric zeta function

2021/10/18 by Li, Jiangtao
#11M32 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2110.09652

Abstract

In this paper we define a symmetric zeta function. We show that it can be analytically continued to a meromorphic function on ℂ³ 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.

Related

• A continuous version of multiple zeta functions and multiple zeta values
• t-adic symmetric multiple zeta values for indices in which 1 and 3 appear alternately
• Analytic continuation of multiple zeta-functions and the asymptotic behavior at non-positive integers
• On the a-points of symmetric sum of multiple zeta function
• Multiple zeta values over global function fields