Class numbers not divisible by 3
by
Michael Rosen
Brown University
Coauthors: Allison Pacelli, Williams College

Let k=F(T), where k is a field with q elements and 3 does not divide q+1. In a paper published in 1988, H. Ichimura gave an explicit construction of infinitley many quadratic extensions K/k such that 3 does not divide the class number of K. In this paper we give a partial generalization of this result. Let m be a positive integer not divisible by 3. Then, for a large class of finite fields, F, we give an explicit construction of infinitely many extensions K/k, of degree m, such that 3 does not divide the class number of K. The expression "a large class of finite fields" will be made precise.

Date received: April 22, 2008