Mordell-Tornheim multiple zeta-functions, their integral analogues, and relations among multiple polylogarithms

2024/09/30 by Kohji Matsumoto, Matsumoto, Kohji, Kazuhiro Onodera +3 · 1 citation
Chemistry · Materials Science · Mathematics · #11M32 #Advanced Mathematical Identities #Crystallography and molecular interactions #FOS: Mathematics #Number Theory (math.NT) #Polymer Synthesis and Characterization

paper · pdf · doi:10.48550/arxiv.2409.19980

openalex publication_date 2024/09/30 · openalex created_date 2024/10/13 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of a multiple series of Mordell-Tornheim type and its integral analogue at x=0. Our approach is to show a relation between the multiple series and its integral analogue by using Abel's summation formula, and to deeply investigate the behavior of the integral analogue. Additionally, we establish some nontrivial relations among multiple polylogarithms by comparing two seemingly different asymptotic formulas for the integral analogue.

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• Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values

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