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

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. For a video summary of this paper, please visit https://youtu.be/Uxk_qbJxQo. [ABSTRACT FROM AUTHOR]