In this paper, we consider the question of correcting mock modular forms in order to obtain p-adic modular forms. In certain cases we show that a mock modular form M is a p-adic modular form. Furthermore, we prove that otherwise the unique correction of M is intimately related to the shadow of M.

In his letter [Ser96], J.-P. Serre proves that the systems of Hecke eigenvalues given by modular forms (mod p) are the same as the ones given by locally constant functions A×B/B × → F̄p, where B is the endomorphism algebra of a supersingular elliptic curve. After giving a detailed exposition of Serre’s result, we prove that the systems of Hecke eigenvalues given by Siegel modular forms (mod p) o...

In this paper, we prove the existence and uniqueness of fixed points for cyclic (α,β)-admissible type F-contraction and F−weak contraction under the setting of modular spaces, where the modular is convex and satisfying the ∆2-condition. Later, we prove some periodic point results for self-mappings on a modular space. We also give some examples to s...