Tempering the polylogarithm

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dc.creatorEpstein, Charles L.
dc.creatorMorava, Jack
dc.date2006-11-08
dc.date.accessioned2026-07-07T07:32:39Z
dc.date.available2026-07-07T07:32:39Z
dc.descriptionWe show that the function Li_s(e^x) extends to an entire function of the complex variable s, taking values in tempered distributions in x on the whole real line. That the classical polylogarithm extends similarly, as an entire function taking values in distributions on compactly-supported functions on the positive real axis, is a corollary. We then identify the singularities of Li_s(e^x) in terms of distribution powers of x; this leads to a simple proof of the smoothness of the `modified' polylogarithm of Bloch, Ramakrishnan, Wigner, Wojtkowiak, Zagier, and others.
dc.descriptionSupported by the DARPA FunBio program
dc.identifierhttps://arxiv.org/abs/math/0611240
dc.identifierhttp://arxiv.org/abs/math/0611240
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119186
dc.subjectClassical Analysis and ODEs
dc.subjectNumber Theory
dc.subject11G55, 46F20
dc.titleTempering the polylogarithm
dc.typetext

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