Eisenstein-Kronecker series via the Poincaré bundle

Abstract

A classical construction of Katz gives a purely algebraic construction of Eisenstein--Kronecker series using the Gauß--Manin connection on the universal elliptic curve. This approach gives a systematic way to study algebraic and $p$-adic properties of real-analytic Eisenstein series. In the first part of this paper we provide an alternative algebraic construction of Eisenstein--Kronecker series via the Poincaré bundle. Building on this, we give in the second part a new conceptional construction of Katz' two-variable $p$-adic Eisenstein measure through $p$-adic theta functions of the Poincaré bundle.

42 pages; small changes and corrections; final version

References in corpus (2)

• Algebraic theta functions and p-adic interpolation of Eisenstein-Kronecker numbers
• On the de Rham and p-adic realizations of the Elliptic Polylogarithm for CM elliptic curves