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On the number of real quadratic fields with class number divisible by 3
Author(s):
K.
Chakraborty;
M.
Ram
Murty
Journal:
Proc. Amer. Math. Soc.
131
(2003),
41-44.
MSC (2000):
Primary 11R29;
Secondary 11R11
Posted:
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  . 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.
References:
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- 1.
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- 2.
- David A. Cardon and M. Ram Murty: Exponents of class groups of quadratic function fields over finite fields, Canadian Math. Bulletin, 44 (2001), 398-407.
- 3.
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- 4.
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- 6.
- T. Honda: A few remarks on class numbers of imaginary quadratic fields, Osaka J. Math., 12 (1975), 19-21. MR 52:8083
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- 8.
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- 9.
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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:
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
Posted:
May 15, 2002
Communicated by:
Dennis A. Hejhal
Copyright of article:
Copyright
2002,
American Mathematical Society
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