p-adic elliptic polylogarithm, p-adic Eisenstein series and Katz measure

Abstract

The specializations of the motivic elliptic polylog are called motivic Eisenstein classes. For applications to special values of L-Functions, it is important to compute the realizations of these classes. In this paper, we prove that the syntomic realization of the motivic Eisenstein classes, restricted to the ordinary locus of the modular curve, may be expressed using p-adic Eisenstein-Kronecker series. These p-adic modular forms are defined using the two-variable p-adic measure with values in p-adic modular forms constructed by Katz.