The syntomic realization of the elliptic polylogarithm via the Poincar\'e bundle

TL;DR

This paper provides an explicit p-adic analytic description of the syntomic elliptic polylogarithm on the universal elliptic curve, extending previous work on syntomic Eisenstein classes.

Contribution

It introduces a new explicit description of the syntomic elliptic polylogarithm using p-adic moment functions related to Katz's Eisenstein measure, generalizing prior results.

Findings

Explicit p-adic description of the elliptic polylogarithm

Extension of previous syntomic Eisenstein class results

Connection to Katz's p-adic Eisenstein measure

Abstract

We give an explicit description of the syntomic elliptic polylogarithm on the universal elliptic curve over the ordinary locus of the modular curve in terms of certain $p$-adic analytic moment functions associated to Katz' two-variable $p$-adic Eisenstein measure. The present work generalizes previous results of Bannai-Kobayashi-Tsuji and Bannai-Kings on the syntomic Eisenstein classes.