On the class number of abelian number fields
著者
書誌事項
On the class number of abelian number fields
Springer, c2019
- タイトル別名
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Über die Klassenzahl abelscher Zahlkörper
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注記
"The book is a translation of the German edition-two chapters are added as reprints"--T.p. verso
"English translation of the German reprint published by Springer-Verlag Berlin, Heidelberg, 1985"--T.p. verso
First published in German: c1952
Includes bibliographical references and index
内容説明・目次
内容説明
With this translation, the classic monograph UEber die Klassenzahl abelscher Zahlkoerper by Helmut Hasse is now available in English for the first time.
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.
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.
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.
目次
Part I.- Introduction.- The Generalized Class Number Formulas.- The Arithmetic Structure of the Class Number Formula for Real Fields.- The Arithmetic Structure of the Relative Class Number Formula for Imaginary Fields.- Appendix: Tables of Relative Class Numbers - Part II.- On the Relative Class Number of the Imaginary Abelian Number Field I.- On the Relative Class Number of the Imaginary Abelian Number Field II.- Supplemental Readings.
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