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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, [email protected]
Yoshiyuki Kitaoka
Affiliation:
Dept. of Math., Meijo University, Tenpaku-ku, Nagoya, 468-8502, Japan, [email protected]
Jing Yu
Affiliation:
Institute of Math., Academia Sinica, Nakang, Taipei, Taiwan, and National Center for Theoretical Science, Hsinchu, Taiwan, [email protected]
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Abstract

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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

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