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Line 3: ==Serre's definition== Serre defined a ''p''-adic modular form to be a formal power series that is a limit of ordinary modular forms with integer coefficients. The weights of these ordinary modular forms need not be the same; in fact, if they are then the ''p''-adic modular form is just a linear combination of ordinary modular forms. In general the weight of a ''p''-adic modular form is a ''p''-adic number, given by the limit of the weights of the ordinary modular forms. ==Katz's definition==

P-adic modular form: Difference between revisions