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

 

Exponents of class groups of real quadratic function fields


Authors: Kalyan Chakraborty and Anirban Mukhopadhyay
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1951-1955
MSC (2000): Primary 11R58; Secondary 11R29
Published electronically: February 18, 2004
MathSciNet review: 2053965
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Abstract: We show that there are $\gg q^{l/(2g)}$ polynomials $D\in\mathbb{F} _q[t]$ with $\deg(D)\le l$ such that the ideal class group of the real quadratic extensions $\mathbb{F} _q(t,\sqrt D)$ has an element of order $g$.


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Additional Information

Kalyan Chakraborty
Affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
Email: kalyan@mri.ernet.in

Anirban Mukhopadhyay
Affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
Address at time of publication: The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600113, India
Email: anirban@mri.ernet.in, anirban@imsc.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07269-7
PII: S 0002-9939(04)07269-7
Keywords: Class group, real quadratic fields
Received by editor(s): September 4, 2002
Received by editor(s) in revised form: April 21, 2003
Published electronically: February 18, 2004
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2004 American Mathematical Society