On the Class Number of Abelian Number Fields
Extended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi
Authors: Hasse, Helmut
Free Preview- First English translation of the original German edition
- Provides systematic tables on the relative class number of imaginary abelian number fields
- Contains rigorous results on the class numbers of abelian number fields
- Offers numerous, deeper, algebraic and number-theoretic details
- Suitable for students of algebraic number theory
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- About this book
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With this translation, the classic monograph Über die Klassenzahl abelscher Zahlkörper 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.
- Table of contents (6 chapters)
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The Generalized Class Number Formulas
Pages 7-21
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The Arithmetic Structure of the Class Number Formula for Real Fields
Pages 23-63
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The Arithmetic Structure of the Relative Class Number Formula for Imaginary Fields
Pages 65-251
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On the Relative Class Number of the Imaginary Abelian Number Field I
Pages 255-305
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On the Relative Class Number of the Imaginary Abelian Number Field II
Pages 307-357
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Table of contents (6 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- On the Class Number of Abelian Number Fields
- Book Subtitle
- Extended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi
- Authors
-
- Helmut Hasse
- Translated by
- Hirabayashi, M.
- Copyright
- 2019
- Publisher
- Springer International Publishing
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-01512-1
- DOI
- 10.1007/978-3-030-01512-1
- Hardcover ISBN
- 978-3-030-01510-7
- Edition Number
- 1
- Number of Pages
- XXXVIII, 365
- Number of Illustrations
- 33 b/w illustrations
- Additional Information
- English translation of the German reprint published by Springer-Verlag Berlin, Heidelberg, 1985
- Topics
