國立高雄大學圖資館 |

Language: English

Back

On the class number of abelian numbe...

Hasse, Helmut.

On the class number of abelian number fieldsextended with tables by Ken-ichi Yoshino and Mikihito Hirabayashi /

Record Type:	Electronic resources : Monograph/item
Title/Author:	On the class number of abelian number fieldsby Helmut Hasse.
Reminder of title:	extended with tables by Ken-ichi Yoshino and Mikihito Hirabayashi /
Author:	Hasse, Helmut.
Published:	Cham :Springer International Publishing :2019.
Description:	xxxviii, 365 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Abelian groups.
Online resource:	https://doi.org/10.1007/978-3-030-01512-1
ISBN:	9783030015121$q(electronic bk.)

On the class number of abelian number fieldsextended with tables by Ken-ichi Yoshino and Mikihito Hirabayashi /
Hasse, Helmut.

On the class number of abelian number fieldsextended with tables by Ken-ichi Yoshino and Mikihito Hirabayashi /[electronic resource] :by Helmut Hasse. - Cham :Springer International Publishing :2019. - xxxviii, 365 p. :ill., digital ;24 cm.

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.

With this translation, the classic monograph Uber die Klassenzahl abelscher Zahlkorper 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.

ISBN: 9783030015121$q(electronic bk.)

Standard No.: 10.1007/978-3-030-01512-1doiSubjects--Topical Terms:

245403
Abelian groups.

LC Class. No.: QA171

Dewey Class. No.: 512.86

On the class number of abelian number fieldsextended with tables by Ken-ichi Yoshino and Mikihito Hirabayashi /
LDR:02679nmm a2200349 a 4500 001 556875
003 DE-He213
005 20190423184630.0
006 m d
007 cr nn 008maaau
008 191127s2019 gw s 0 eng d
020 $a 9783030015121$q(electronic bk.)
020 $a 9783030015107$q(paper)
024 7 $a 10.1007/978-3-030-01512-1 $2 doi
026 4 3 $a nam a2200337 a 4500
035 $a 978-3-030-01512-1
040 $a GP $c GP
041 1 $a eng $h ger
050 4 $a QA171
072 7 $a PBH $2 bicssc
072 7 $a MAT022000 $2 bisacsh
072 7 $a PBH $2 thema
082 0 4 $a 512.86 $2 23
090 $a QA171 $b .H354 2019
100 1 $a Hasse, Helmut. $3 839226
240 1 0 $a Uber die Klassenzahl abelscher Zahlkorper. $l English
245 1 0 $a On the class number of abelian number fields $h [electronic resource] : $b extended with tables by Ken-ichi Yoshino and Mikihito Hirabayashi / $c by Helmut Hasse.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xxxviii, 365 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a With this translation, the classic monograph Uber die Klassenzahl abelscher Zahlkorper 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.
650 0 $a Abelian groups. $3 245403
650 1 4 $a Number Theory. $3 274059
650 2 4 $a Field Theory and Polynomials. $3 274058
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-030-01512-1
950 $a Mathematics and Statistics (Springer-11649)