Une notion de multizêtas finis associée au Frobenius du groupe fondamental de P1\{0,1,∞}

Translated title of the contribution: A notion of finite multiple zeta values associated with the Frobenius of the fundamental group of P1\{0,1,∞}

David Jarossay

Research output: Contribution to journalArticlepeer-review

Abstract

We show that multiple harmonic sums of the form. ∑apk<n1<. . .<nd<(a+1)pk1n1s1. . .ndsd,for a∈Z,k∈N*,sd,. . .,s1∈N*, admit a simple canonical expansion in terms of p-adic multiple zeta values. More generally, we interpret geometrically the multiplication by p of the upper bound of a multiple harmonic sum. This is equivalent to the inversion of the sums of series that express p-adic multiple zeta values. The result leads to the definition of a notion of finite multiple zeta values that is of geometric origin; it gives a framework to study the algebraic properties of those multiple harmonic sums whose upper bound is a power of a prime number. The result also has applications to a conjecture of Kaneko and Zagier.

Translated title of the contributionA notion of finite multiple zeta values associated with the Frobenius of the fundamental group of P1\{0,1,∞}
Original languageFrench
Pages (from-to)877-882
Number of pages6
JournalComptes Rendus Mathematique
Volume353
Issue number10
DOIs
StatePublished - 1 Oct 2015
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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