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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Class numbers of quadratic fields ${\mathbb Q}(\sqrt{D})$ and ${\mathbb Q}(\sqrt{tD})$


Author: Dongho Byeon
Journal: Proc. Amer. Math. Soc. 132 (2004), 3137-3140
MSC (2000): Primary 11R11, 11R29
Published electronically: June 21, 2004
MathSciNet review: 2073286
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Abstract: Let $t$ be a square free integer. We shall show that there exist infinitely many positive fundamental discriminants $D>0$ with a positive density such that the class numbers of quadratic fields ${\mathbb Q}(\sqrt{D})$ and ${\mathbb Q}(\sqrt{tD})$ are both not divisible by 3.


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Additional Information

Dongho Byeon
Affiliation: School of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: dhbyeonmath.snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07536-7
PII: S 0002-9939(04)07536-7
Received by editor(s): December 23, 2002
Published electronically: June 21, 2004
Additional Notes: This work was supported by grant No. R08-2003-000-10243-0 from the Basic Research Program of the Korea Science $&$ Engineering Foundation
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2004 American Mathematical Society