Remark on a symmetric zeta function

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.

28 pages

References in corpus (1)

• Rational convex cones and cyclotomic multiple zeta values