On the Class Number of Abelian Number FieldsExtended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi【電子書籍】[ Helmut Hasse ]

＜p＞With this translation, the classic monograph ＜em＞?ber die Klassenzahl abelscher Zahlk?rper＜/em＞ by Helmut Hasse is now available in English for the first time.＜/p＞ ＜p＞The book addresses three main topics: class number formulas for abelian number fields; expressions of the class number of real abelian number fields by the index of the subgroup generated by cyclotomic units; and the Hasse unit index of imaginary abelian number fields, the integrality of the relative class number formula, and the class number parity.＜/p＞ ＜p＞Additionally, the book includes reprints of works by Ken-ichi Yoshino and Mikihito Hirabayashi, which extend the tables of Hasse unit indices and the relative class numbers to imaginary abelian number fields with conductor up to 100.＜/p＞ ＜p＞The text provides systematic and practical methods for deriving class number formulas, determining the unit index and calculating the class number of abelian number fields. A wealth of illustrative examples, together with corrections and remarks on the original work, make this translation a valuable resource for today’s students of and researchers in number theory.＜/p＞画面が切り替わりますので、しばらくお待ち下さい。

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