عنوان

On the class number of abelian number fields :

(Number (ISBN

3030015106

(Number (ISBN

3030015114

(Number (ISBN

3030015122

(Number (ISBN

9783030015107

(Number (ISBN

9783030015114

(Number (ISBN

9783030015121

Erroneous ISBN

9783030015107

Title Proper

On the class number of abelian number fields :

General Material Designation

[Book]

Other Title Information

extended with tables by Ken-ichi Yoshino and Mikihito Hirabayashi /

First Statement of Responsibility

Helmut Masse.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

[2019]

Specific Material Designation and Extent of Item

1 online resource

Text of Note

Includes bibliographical references and index.

Text of Note

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.

0

Text of Note

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.

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030015121

International Standard Book Number

9783030015107

International Standard Book Number

9783030015114

General Material Designation

Über die Klassenzahl abelscher Zahlkörper.

Language (when part of a heading)

English

Abelian groups.

Abelian groups.

MATHEMATICS-- Algebra-- Intermediate.

MAT-- 002040

PBH

PBH

Number

Edition

Class number

Hasse, Helmut,1898-1979

Hirabayashi, Mikihito

Yoshino, Ken-ichi

Date of Transaction

20200823073118.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y