Finite and \'etale polylogarithms
Kenji Sakugawa, Shin-ichiro Seki
TL;DR
This paper establishes an explicit formula connecting étale polylogarithms and finite polylogarithms, extending known relationships in p-adic and algebraic polylogarithm theories.
Contribution
It provides the first explicit formula relating étale and finite polylogarithms, bridging two important classes of polylogarithmic functions.
Findings
Derived an explicit formula relating étale and finite polylogarithms
Extended Besser's formula to an étale setting
Bridged concepts in algebraic and p-adic polylogarithm theories
Abstract
We show an explicit formula relating \'etale polylogarithms introduced by Wojtkowiak and finite polylogarithms introduced by Elbaz-Vincent and Gangl. This formula is an \'etale analog of Besser's formula relating Coleman's -adic polylogarithms and the finite polylogarithms.
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Taxonomy
TopicsAdvanced Mathematical Identities · Algebraic Geometry and Number Theory · Analytic Number Theory Research