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

 

On the number of real quadratic fields with class number divisible by 3


Authors: K. Chakraborty and M. Ram Murty
Journal: Proc. Amer. Math. Soc. 131 (2003), 41-44
MSC (2000): Primary 11R29; Secondary 11R11
Published electronically: May 15, 2002
MathSciNet review: 1929021
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Abstract: We find a lower bound for the number of real quadratic fields whose class groups have an element of order $3$. More precisely, we establish that the number of real quadratic fields whose absolute discriminant is $\leq x$ and whose class group has an element of order $3$ is $\gg x^{\frac{5}{6}}$ improving the existing best known bound $\gg x^{\frac{1}{6}}$ of R. Murty.


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Additional Information

K. Chakraborty
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Address at time of publication: Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, U. P., India
Email: kalyan@mast.queensu.ca, kalyan@mri.ernet.in

M. Ram Murty
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Email: murty@mast.queensu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06603-0
PII: S 0002-9939(02)06603-0
Keywords: Class group, real quadratic fields
Received by editor(s): August 15, 2001
Published electronically: May 15, 2002
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2002 American Mathematical Society