Cyclotomic p-adic Multi-Zeta Values in Depth Two

2013/02/26 by Sı̇nan Ünver, Sinan Unver, Unver, Sinan · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1302.6406

arxiv created 2013/02/26 · openalex publication_date 2013/02/26 · arxiv updated 2013/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we compute the values of the p-adic multiple polylogarithms of depth two at roots of unity. Our method is to solve the fundamental differential equation satisfied by the crystalline frobenius morphism using rigid analytic methods. The main result could be thought of as a computation in the p-adic theory of higher cyclotomy. We expect the result to be useful in proving non-vanishing results since it gives quite explicit formulas.

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• p-adic multiple zeta values and p-adic pro-unipotent harmonic\n actions : summary of parts I and II

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