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Mathematics of Computation

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Class group frequencies
of real quadratic function fields:
The degree 4 case

Author: Christian Friesen
Journal: Math. Comp. 69 (2000), 1213-1228
MSC (1991): Primary 11R29, 11R58, 11R11
Published electronically: May 24, 1999
MathSciNet review: 1659859
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Abstract: The distribution of ideal class groups of $\mathbb{F}_{q}(T,\sqrt {M(T)})$ is examined for degree-four monic polynomials $M \in \mathbb{F}_{q}[T]$ when $\mathbb{F}_{q}$ is a finite field of characteristic greater than 3 with $q \in [20000,100000]$ or $q \in [1020000,1100000]$ and $M$ is irreducible or has an irreducible cubic factor. Particular attention is paid to the distribution of the $p$-Sylow part of the class group, and these results agree with those predicted using the Cohen-Lenstra heuristics to within about 1 part in 10000. An alternative set of conjectures specific to the cases under investigation is in even sharper agreement.

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Additional Information

Christian Friesen
Affiliation: Ohio State University at Marion,1465 Mt. Vernon Ave, Marion, Ohio 43302

Keywords: Class groups, Cohen-Lenstra conjecture, function fields, class numbers
Received by editor(s): September 8, 1998
Published electronically: May 24, 1999
Article copyright: © Copyright 2000 American Mathematical Society