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

Abstract. The distribution of ideal class groups of Fq(T, M(T)) is examined for degree-four monic polynomials M Fq[T] when Fq is a finite field of characteristic greater than 3 with q [20000, 100000] or q [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.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Christian Friesen
• Keywords: Class Group, Degree-four Monic Polynomials, Ideal Class Groups, MOC 2000