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On the Second Class Group of Real Quadratic Number Fields

  • This thesis generalizes the Cohen-Lenstra heuristic for the class groups of real quadratic number fields to higher class groups. A "good part" of the second class group is defined. In general this is a non abelian proper factor group of the second class group. Properties of those groups are described, a probability distribution on the set of those groups is in- troduced and proposed as generalization of the Cohen-Lenstra heuristic for real quadratic number fields. The calculation of number field tables which contain information about higher class groups is explained and the tables are compared to the heuristic. The agree- ment is close. A program which can create an internet database for number field tables is presented.

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Author:Maximilian Boy
URN (permanent link):urn:nbn:de:hbz:386-kluedo-28856
Advisor:Gunter Malle
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2012/02/22
Year of Publication:2012
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2012/02/22
Date of the Publication (Server):2012/02/20
Tag:Cohen-Lenstra heuristic; probability distribution; real quadratic number fields; second class group
Number of page:78
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):11-XX NUMBER THEORY / 11Rxx Algebraic number theory: global fields (For complex multiplication, see 11G15) / 11R29 Class numbers, class groups, discriminants
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 15.02.2012