Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-06-01T23:49:17.599Z Has data issue: false hasContentIssue false
  • English
  • Français

Distribution of units of real quadratic number fields

Published online by Cambridge University Press:  22 January 2016

Yen-Mei J. Chen ,
Yoshiyuki Kitaoka  and
Jing Yu
Yen-Mei J. Chen
Affiliation:
Dept. of Math., Tamkang University, Tamshui, Taipei, Taiwan, ymjchen@mail.tku.edu.tw
Yoshiyuki Kitaoka
Affiliation:
Dept. of Math., Meijo University, Tenpaku-ku, Nagoya, 468-8502, Japan, kitaoka@meijo-u.ac.jp
Jing Yu
Affiliation:
Institute of Math., Academia Sinica, Nakang, Taipei, Taiwan, and National Center for Theoretical Science, Hsinchu, Taiwan, yu@math.sinica.edu.tw
Rights & Permissions [Opens in a new window]

Abstract

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.

Let k be a real quadratic field and k, E the ring of integers and the group of units in k. Denoting by E() the subgroup represented by E of (k/)× for a prime ideal , we show that prime ideals for which the order of E() is theoretically maximal have a positive density under the Generalized Riemann Hypothesis.

Keywords

11R45
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 158 , December 2000 , pp. 167 - 184
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2000

References

[H] Hooley, C., On Artin’s conjecture, J. reine angew. Math., 225 (1967), 209–220.Google Scholar
[IK] Ishikawa, M. and Kitaoka, Y., On the distribution of units modulo prime ideals in real quadratic fields, J. reine angew. Math., 494 (1998), 65–72.Google Scholar
[LO] Lagarias, J. C. and Odlyzko, A. M., Effective version of the Chebotarev density theorem, Algebraic Number Fields (Fröhlich, ed.), Academic Press (1977), 409–464.Google Scholar
[M] Masima, K., On the distribution of units in the residue class field of real quadratic fields and Artin’s conjecture (in Japanese), RIMS Kokyuroku, 1026 (1998), 156–166.Google Scholar
[S] Serre, J. P., Quelques applications du théorème de densité de Chebotarev, I.H.E.S., 54 (1981), 323–401.Google Scholar