On functions of Arakawa and Kaneko and multiple zeta functions

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dc.creatorKuba, Markus
dc.date2009-03-26
dc.date.accessioned2026-07-07T12:57:02Z
dc.date.available2026-07-07T12:57:02Z
dc.descriptionWe study for $s\in\N=\{1,2,...\}$ the functions $ξ_{k}(s)=\frac{1}{Γ(s)}\int_{0}^{\infty}\frac{t^{s-1}}{e^t-1}\Li_{k}(1-e^{-t})dt$, and more generally $ξ_{k_1,...,k_r}(s)=\frac{1}{Γ(s)}\int_{0}^{\infty}\frac{t^{s-1}}{e^t-1}\Li_{k_1,...,k_r}(1-e^{-t})dt$, introduced by Arakawa and Kaneko \cite{Arakawa} and relate them with (finite) multiple zeta functions, partially answering a question of \cite{Arakawa}. In particular, we give an alternative proof of a result of Ohno \cite{Ohno2}.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/0903.4552
dc.identifierhttp://arxiv.org/abs/0903.4552
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224790
dc.subjectNumber Theory
dc.subject11M06, 40B05
dc.titleOn functions of Arakawa and Kaneko and multiple zeta functions
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