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Indivisibility of Class Numbers of Real Quadratic Fields
Authors:Ken Ono
Institution:(1) Department of Mathematics, Penn. State University, University, Park, PA 16802, U.S.A.; e-mail
Abstract: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 lsquoCohen and Lenstra Heuristicsrsquo give a probability that pnmidh(D). If pgt;3 is prime, then subject to a mild condition, we show that

$$\# \left\{ {0 < D < X|p\nmid h(D)} \right\} \gg _p \frac{{\sqrt X }}{{\log X}}.$$
This condition holds for each 3<p<5000.
Keywords:class numbers of real quadratic fields  
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