Additive number theory and the Dyson transform

In 1942 Mann solved a famous problem, the \alpha+\beta conjecture, about the lower bound of the Shnirel'man density of sums of sets of positive integers. In 1945, Dyson generalized Mann's theorem and obtained a lower bound for the Shnirel'man density of rank r sumsets. His proof introduced the Dyson transform,... Show more