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Line 4: ==Serre's definition== Serre defined a ''p''-adic modular form to be a formal power series with ''p''-adic coefficients that is a ''p''-adic limit of ~~ordinary~~classical modular forms with integer coefficients. The weights of these ~~ordinary~~classical modular forms need not be the same; in fact, if they are then the ''p''-adic modular form is nothing more than a linear combination of ~~ordinary~~classical 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~~classical modular forms. The ''p''-adic modular forms defined by Serre are special cases of those defined by Katz.

P-adic modular form: Difference between revisions