On p-adic analogue of Weil's elliptic functions according to Eisenstein

Abstract

In this paper, using p-adic integration with values in spaces of modular forms, we construct the p-adic analogue of Weil's elliptic functions according to Eisenstein in the book “Elliptic Functions According to Eisenstein and Kronecker”. This construction extends Serre's p-adic family of Eisenstein series in “Formes modulaires et fonctions zêta p-adiques”. We show that the power series expansion of Weil's elliptic functions also exists in the p-adic case.