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{{DISPLAYTITLE:''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. {{harvtxt|Serre|1973}} introduced ''p''-adic modular forms as limits of ordinary modular forms, and {{harvtxt|Katz|1973}} 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'''.
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