#### Vol. 14, No. 7, 2020

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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
##### 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 ${ℙ}^{1}\setminus \left\{0,{\mu }_{N},\infty \right\}$. 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.

##### 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
Primary: 11G99