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arXiv · 1503.08756

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

David Jarossay
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Abstract

We generalize the definition of overconvergent $p$-adic multiple polylogarithms and of $p$-adic cyclotomic multiple zeta values and we prove a bound on their norm. A byproduct of the proof is a characterization of these objects in terms of certain regularized $p$-adic iterated integrals. The generalization of the definition consists in replacing the underlying Frobenius structure by its iterations. The bound on the norms of overconvergent $p$-adic multiple polylogarithms that we obtain is a prerequisite for our subsequent papers on $p$-adic cyclotomic multiple zeta values.

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David Jarossay. 2018-08-28. A bound on the norm of overconvergent $p$-adic multiple polylogarithms. https://doi.org/10.1016/j.jnt.2019.04.026

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