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

[摘要] Text. 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. Video. For a video summary of this paper, please visit https://youtu.be/Uxk_qbJxQo. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] p-adic differential equations;Knizhnik-Zamolodchikov equations;Crystalline pro-unipotent fundamental groupoid;The projective line minus three points;p-adic cyclotomic multiple zeta values;Overconvergent p-adic multiple polylogarithms;Cyclotomic multiple harmonic sums