Imaginary Quadratic Fields with Small Odd Class Number, by Steven Arno, M. L. Robinson, and Ferrell S. Wheeler

This paper has appeared in Acta Arith. 83 (1998), no. 4, 295-330 and so the dvi version has been removed. In this paper we solve the class number m problem for the ten odd values of m between 5 and 23. "Large" discriminants are ruled out using a result of Oesterle. Methods of Stark and Montgomery-Weinberger are used to treat a portion of the discriminants of "medium" size. In order to eliminate the remaining, smaller discriminants of "medium" size, we introduce new methods which partition the space of minima (of reduced quadratic forms of given negative fundamental discriminant) in a tractable manner. "Small" discriminants are treated by combining the new minima partitions with a computationally intensive sieve.

Steven Arno <arno@super.org>
M. L. Robinson <robinson@super.org>
Ferrell S. Wheeler <wheeler@super.org>