Quasimodular Siegel Modular Forms as P-Adic Modular Forms

Abstract

There is a sophisticated theory of nearly holomorphic Siegel modular forms by Shimura. Using previous results by Nagaoka and myself on Rankin-Cohen operators and theta-operators we will present a proof that quasimodular forms (defined as constant terms or as holomorphic part of a nearly holomorphic Siegel modular form) are always p-adic. * This paper was presented at the International Scientific Conference Graded structures in algebra and their applications, dedicated to the memory of Prof. Marc Krasner, IUCDubrovnik, Croatia, September, 22-24, 2016.