Pro-unipotent harmonic actions and dynamical properties of p-adic cyclotomic multiple zeta values

Jarossay, David

doi:10.2140/ant.2020.14.1711

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Pro-unipotent harmonic actions and dynamical properties of $p$-adic cyclotomic multiple zeta values

David Jarossay

Vol. 14 (2020), No. 7, 1711–1746

DOI: 10.2140/ant.2020.14.1711

Abstract

$p$ -adic cyclotomic multiple zeta values depend on the choice of a number of iterations of the crystalline Frobenius of the pro-unipotent fundamental groupoid of $ℙ^{1} ∖ {0, μ_{N}, \infty}$ . In this paper we study how the iterated Frobenius depends on the number of iterations, in relation with the computation of $p$ -adic cyclotomic multiple zeta values in terms of cyclotomic multiple harmonic sums. This provides new results on that computation and the definition of a new pro-unipotent harmonic action.

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Keywords

$p$-adic cyclotomic multiple zeta values, cyclotomic multiple harmonic sums, pro-unipotent harmonic actions, projective line minus three points, pro-unipotent fundamental groupoid, crystalline Frobenius

Mathematical Subject Classification 2010

Primary: 11G99

Milestones

Received: 26 August 2018

Revised: 23 December 2019

Accepted: 23 February 2020

Published: 18 August 2020

Authors

David Jarossay
Department of Mathematics Ben Gurion University of the Negev Be’er-Sheva‘ Israel

Vol. 14, No. 7, 2020