Values and derivative values at nonpositive integers of generalized multiple Hurwitz zeta functions

2023/12/07 by Simon Rutard, Rutard, Simon · 1 citation
Mathematics · #2020: Primary 11M32 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Secondary 11M41

paper · pdf · doi:10.48550/arxiv.2312.04725

openalex publication_date 2023/12/07 · openalex created_date 2023/12/12 · openalex updated_date 2026/07/28

Abstract

We establish the meromorphic continuation of certain multiple zeta functions of generalized Hurwitz type. From this meromorphic continuation, we obtain explicit formulas for their (derivative) values at nonpositive integers along a given direction. As an application, we provide explicit formulas for some values and derivative values of the Witten zeta functions ζ_\mathfrakg₂ and ζ_\mathfrakso(5). Furthermore, by employing a Meinardus-type theorem, we investigate the asymptotic behavior of the number of n-dimensional representations of the exceptional Lie algebra \mathfrakg₂.

Citations

• On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function

Cited by

• Values at non-positive integers of partially twisted multiple zeta-functions II

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