Taylor coefficients of Anderson-Thakur series and explicit formulae

2019/02/19 by Chieh-Yu Chang, Chang, Chieh-Yu, Nathan Green +3
Mathematics · #11G09 #11M32 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1902.06879

openalex publication_date 2019/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each positive characteristic multiple zeta value (defined by Thakur), the first and third authors constructed a t-module together with an algebraic point such that a specified coordinate of the logarithmic vector of the algebraic point is a rational multiple of that multiple zeta value. The objective of this paper is to use the Taylor coefficients of Anderson-Thakur series and t-motivic Carlitz multiple star polylogarithms to give explicit formulae for all of the coordinates of this logarithmic vector.

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