Class group frequencies of real quadratic function fields: The degree 4 case
Christian Friesen · Mathematics of Computation · 1999
The distribution of ideal class groups of F q ( T , M ( T ) ) \mathbb {F}_{q}(T,\sqrt {M(T)}) is examined for degree-four monic polynomials M ∈ F q [ T ] M \in \mathbb {F}_{q}[T] when F q \mathbb {F}_{q} is a finite field of characteristic greater than 3 with q ∈ [ 20000 , 100000 ] q \in [20000,100000] or q ∈ [ 1020000 , 1100000 ] q \in [1020000,1100000] and M M is irreducible or has an irreducible cubic factor. Particular attention is paid to the distribution of the p 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.