Vol. 14, No. 3, 2020

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The algebraic de Rham realization of the elliptic polylogarithm via the Poincaré bundle

Johannes Sprang

Vol. 14 (2020), No. 3, 545–585
Abstract

We describe the algebraic de Rham realization of the elliptic polylogarithm for arbitrary families of elliptic curves in terms of the Poincaré bundle. Our work builds on previous work of Scheider and generalizes results of Bannai, Kobayashi and Tsuji, and Scheider. As an application, we compute the de Rham–Eisenstein classes explicitly in terms of certain algebraic Eisenstein series.

Keywords
de Rham cohomology, polylogarithm, Eisenstein classes
Mathematical Subject Classification 2010
Primary: 11G55
Secondary: 14H52
Milestones
Received: 26 February 2018
Revised: 25 June 2019
Accepted: 8 November 2019
Published: 1 June 2020
Authors
Johannes Sprang
Fakultät für Mathematik
Universität Regensburg
Germany