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

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 ${\mathbb{P}}^1-\{0,{\mu }_N,\infty \}$. 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.

27 pages. Part I-3 of "$p$-adic cyclotomic multiple zeta values and $p$-adic pro-unipotent harmonic actions"

References in corpus (1)

• A bound on the norm of overconvergent $p$-adic multiple polylogarithms