Khinchin Families and Hayman Class

Abstract

We give criteria, following Hayman and Báez-Duarte, for non-vanishing functions with non-negative coefficients to be Gaussian and strongly Gaussian. We use these criteria to show in a simple and unified manner asymptotics for a number of combinatorial objects, and, particularly, for a variety of partition questions like Ingham’s theorem on partitions with parts in an arithmetic sequence, or Wright’s theorem on plane partitions and, of course, Hardy–Ramanujan’s partition theorem