About: P-adic modular form

In mathematics, a p-adic modular form is a p-adic analog of a modular form, with coefficients that are p-adic numbers rather than complex numbers. introduced p-adic modular forms as limits of ordinary modular forms, and shortly afterwards gave a geometric and more general definition. Katz's p-adic modular forms include as special cases classical p-adic modular forms, which are more or less p-adic linear combinations of the usual "classical" modular forms, and overconvergent p-adic modular forms, which in turn include Hida's ordinary modular forms as special cases.