Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T23:10:19.462Z Has data issue: false hasContentIssue false
  • English
  • Français

Two theorems on the class number of positive definite quadratic forms

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka
Yoshiyuki Kitaoka*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note we study the estimate from above and below and the asymptotic behaviour of the class number of positive definite integral quadratic forms.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 51 , September 1973 , pp. 79 - 89
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Curtis, C. W. and Reiner, I., Representation theory of finite groups and associative algebras, Interscience Pub., 1962.Google Scholar
[2] Kneser, M., Klassenzahlen quadratischer Formen, Jahresbericht d. DMV, 61 (1958), 76–88.Google Scholar
[3] Körner, O., Die Maße der Geschlechter quadratischer Formen vom Range ≤ 3 in quadratischen Zahlkörpern, Math. Ann., 193 (1971), 279–314.CrossRefGoogle Scholar
[4] Minkowski, H., Diskontinuitätsbereich für arithmetische Aquivalenz, J. reine angew. Math., 129 (1905), 220–274.CrossRefGoogle Scholar
[5] O’Meara, O. T., Introduction to quadratic forms, Springer-Verlag, 1963.CrossRefGoogle Scholar
[6] Pfeuffer, H., Einklassige Geschlechter totalpositiver quadratischer Formen in totalreellen algebraischen Zahlkörpern, Jour, number theory 3 (1971), 371–411.CrossRefGoogle Scholar
[7] Siegel, C. L., Über die analytische Theorie der quadratischen Formen, Ann. Math., 36 (1935), 527–606.CrossRefGoogle Scholar
[8] Siegel, CL., Einheiten quadratischer Formen, Abh. Math. Sem. Univ. Hamburg, 13 (1940), 209–239.CrossRefGoogle Scholar
[9] Weil, A., Discontinuous subgroups of classical groups, Lecture at the University of Chicago, 1958.Google Scholar