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In number theory, a Hecke character is a generalisation of a Dirichlet character, introduced by Erich Hecke to construct a class of ''L''-functions larger than Dirichlet ''L''-functions, and a natural setting for the Dedekind zeta-functions and certain others which have functional equations analogous to that of the Riemann zeta-function. A name sometimes used for ''Hecke character'' is the German term Größencharakter (often written Grössencharakter, Grossencharacter, etc.). ==Definition using ideles== A Hecke character is a character of the idele class group of a number field or global function field. It corresponds uniquely to a character of the idele group which is trivial on principal ideles, via composition with the projection map. This definition depends on the definition of a character, which varies slightly between authors: It may be defined as a homomorphism to the non-zero complex numbers (also called a "quasicharacter"), or as a homomorphism to the unit circle in C ("unitary"). Any quasicharacter (of the idele class group) can be written uniquely as a unitary character times a real power of the norm, so there is no big difference between the two definitions. The conductor of a Hecke character χ is the largest ideal ''m'' such that χ is a Hecke character mod ''m''. Here we say that χ is a Hecke character mod ''m'' if χ (considered as a character on the idele group) is trivial on the group of finite ideles whose every v-adic component lies in 1 + ''m''Ov. 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「Hecke character」の詳細全文を読む スポンサード リンク
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