The purpose of this article is to use rigid analysis to clarify the relation between classical modular forms and Katz’s overconvergent forms. In particular, we prove a conjecture of F. Gouvêa [G, Conj. 3] which asserts that every overconvergent p-adic modular form of sufficiently small slope is classical. More precisely, let p > 3 be a prime, K a complete subfield of Cp, N be a positive integer...

The theory of p-adic modular forms was developed by J.-P. Serre [8] and N. Katz [5]. This theory is by now considered classical. Investigation of p-adic congruences for modular forms of half-integer weight was carried out by N. Koblitz [6] and led him to deep conjectures. It seems natural to search for p-adic properties of other types of automorphic forms. In this paper we use the Serre approac...

Abstract. Let p be a prime for which the congruence group Γ0(p) ∗ is of genus zero, and j∗ p be the corresponding Hauptmodul. Let f be a nearly holomorphic modular form of weight 1/2 on Γ0(4p) which satisfies some congruence condition on its Fourier coefficients. We interpret f as a vector valued modular form. Applying Borcherds lifting of vector valued modular forms we construct infinite produ...