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

Authors:	Christian Friesen

Institution:	Ohio State University at Marion,1465 Mt. Vernon Ave, Marion, Ohio 43302

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 is irreducible or has an irreducible cubic factor. Particular attention is paid to the distribution of the -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.

Keywords:	Class groups Cohen-Lenstra conjecture function fields class numbers

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