Finite and p-adic polylogarithms

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dc.creatorBesser, Amnon
dc.date2000-06-07
dc.date.accessioned2026-07-07T04:35:46Z
dc.date.available2026-07-07T04:35:46Z
dc.descriptionThe finite n-th polylogarithm li_n(z) in Z/p[z] is defined as the sum on k from 1 to p-1 of z^k/k^n. We state and prove the following theorem. Let Li_k:C_p to C_p be the p-adic polylogarithms defined by Coleman. Then a certain linear combination F_n of products of polylogarithms and logarithms, with coefficients which are independent of p, has the property that p^{1-n} DF_n(z^p) reduces modulo p>n+1 to li_{n-1}(z) where D is the Cathelineau operator z(1-z) d/dz. A slightly modified version of this theorem was conjectured by Kontsevich. This theorem is used by Elbaz-Vincent and Gangl to deduce functional equations of finite polylogarithms from those of complex polylogarithms.
dc.description7 pages, latex2e with amsart class
dc.identifierhttps://arxiv.org/abs/math/0006051
dc.identifierhttp://arxiv.org/abs/math/0006051
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59367
dc.subjectNumber Theory
dc.subjectK-Theory and Homology
dc.titleFinite and p-adic polylogarithms
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