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

Friesen, Christian

doi:10.1090/S0025-5718-99-01154-0

Class group frequencies of real quadratic function fields: The degree 4 case
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Math. Comp. 69 (2000), 1213-1228 Request permission

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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