Revision as of 19:05, 29 November 2012 edit R.e.b. (talk \| contribs) Extended confirmed users, Pending changes reviewers 42,907 edits →Serre's definition: Expanding article ← Previous edit		Revision as of 19:07, 29 November 2012 edit undo R.e.b. (talk \| contribs) Extended confirmed users, Pending changes reviewers 42,907 edits →Serre's definition: Expanding article Next edit →
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 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~~nothing more than 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. The ''p''-adic modular forms defined by Serre are special cases of those defined by Katz.

P-adic modular form: Difference between revisions