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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク P-adic modular form ： ウィキペディア英語版 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. ==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 classical modular forms with integer coefficients. The weights of these 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 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 classical modular forms (in fact a slight refinement gives a weight in Z''p''×Z/(''p''–1)Z). The ''p''-adic modular forms defined by Serre are special cases of those defined by Katz. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「P-adic modular form」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.