Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers
Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers
We study analytic properties of multiple zeta-functions of generalized Hurwitz-Lerch type. First, as a special type of them, we consider multiple zeta-functions of generalized Euler-Zagier-Lerch type and investigate their analytic properties which were already announced in our previous paper. Next we give `desingularization' of multiple zeta-functions of generalized Hurwitz-Lerch type, which include those of generalized Euler-Zagier-Lerch type, the Mordell-Tornheim type, and so on. As a result, the desingularized multiple zeta-function turns out to be an entire function and can be expressed as a finite sum of ordinary multiple zeta-functions of the same type. As applications, we explicitly compute special values of desingularized double zeta-functions of Euler-Zagier type. We also extend our previous results concerning a relationship between $p$-adic multiple $L$-functions and $p$-adic multiple star polylogarithms to more general indices with arbitrary (not necessarily all positive) integers.
Yasushi Komori、Hirofumi Tsumura、Kohji Matsumoto、Hidekazu Furusho
数学
Yasushi Komori,Hirofumi Tsumura,Kohji Matsumoto,Hidekazu Furusho.Desingularization of multiple zeta-functions of generalized Hurwitz-Lerch type and evaluation of p-adic multiple L-functions at arbitrary integers[EB/OL].(2014-04-18)[2025-08-03].https://arxiv.org/abs/1404.4758.点此复制
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