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

DOI:
https://doi.org/10.1090/S0002-9939-02-06603-0

Published electronically:
May 15, 2002

MathSciNet review:
1929021

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Abstract | References | Similar Articles | Additional Information

Abstract: We find a lower bound for the number of real quadratic fields whose class groups have an element of order . More precisely, we establish that the number of real quadratic fields whose absolute discriminant is and whose class group has an element of order is improving the existing best known bound 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:
https://doi.org/10.1090/S0002-9939-02-06603-0

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