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

Kohji Matsumoto; Kazuhiro Onodera; Dilip K. Sahoo

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

Number Theory 2026-03-13 v3

Authors: Kohji Matsumoto , Kazuhiro Onodera , Dilip K. Sahoo

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.

Keywords

multiple zeta values zeta values and euler sums zeta functions

Cite

@article{arxiv.2409.19980,
  title  = {Mordell-Tornheim multiple zeta-functions, their integral analogues, and relations among multiple polylogarithms},
  author = {Kohji Matsumoto and Kazuhiro Onodera and Dilip K. Sahoo},
  journal= {arXiv preprint arXiv:2409.19980},
  year   = {2026}
}

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30pages

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

Abstract

Keywords

Cite

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