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On the Class Number of Abelian Number Fields

Extended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi

Authors: Hasse, Helmut

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  • 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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eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-030-01512-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-030-01510-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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)

Table of contents (6 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-030-01512-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-030-01510-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
On the Class Number of Abelian Number Fields
Book Subtitle
Extended with Tables by Ken-ichi Yoshino and Mikihito Hirabayashi
Authors
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