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2000 Distribution of units of real quadratic number fields
Yen-Mei J. Chen, Yoshiyuki Kitaoka, Jing Yu
Nagoya Math. J. 158: 167-184 (2000).

Abstract

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

Citation

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Yen-Mei J. Chen. Yoshiyuki Kitaoka. Jing Yu. "Distribution of units of real quadratic number fields." Nagoya Math. J. 158 167 - 184, 2000.

Information

Published: 2000
First available in Project Euclid: 27 April 2005

zbMATH: 0984.11057
MathSciNet: MR1766568

Subjects:
Primary: 11R45
Secondary: 11R11, 11R27, 11R47

Rights: Copyright © 2000 Editorial Board, Nagoya Mathematical Journal

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