Indivisibility of Class Numbers of Real Quadratic Fields

Ken Ono

doi:10.1023/A:1001533613223

Abstract

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Let D denote the fundamental discriminant of a real quadratic field, and let h(D) denote its associated class number. If p is prime, then the ’Cohen and Lenstra Heuristics‘ give a probability that p[nmid]h(D). If p>3 is prime, then subject to a mild condition, we show that $\# \{0<D<X|p\nmid h(D)\}\gg_p \frac{\sqrt{X}}{\log X}.$ This condition holds for each 3<p<5000.

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Indivisibility of Class Numbers of Real Quadratic Fields

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Indivisibility of Class Numbers of Real Quadratic Fields

Abstract

Keywords

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