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In number theory, the class number formula relates many important invariants of a number field to a special value of its Dedekind zeta function. ==General statement of the class number formula== We start with the following data: * is a number field. * , where denotes the number of real embeddings of , and is the number of complex embeddings of . * is the Dedekind zeta function of . * is the class number, the number of elements in the ideal class group of . * is the regulator of . * is the number of roots of unity contained in . * is the discriminant of the extension . Then: :Theorem (Class Number Formula). converges absolutely for and extends to a meromorphic function defined for all complex with only one simple pole at , with residue :: This is the most general "class number formula". In particular cases, for example when is a cyclotomic extension of , there are particular and more refined class number formulas. 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「Class number formula」の詳細全文を読む スポンサード リンク
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