Sums of dilates

Abstract

The lambda-dilate of a set A is lambda*A={lambda a : a \in A}. We give an asymptotically sharp lower bound on the size of sumsets of the form lambda_1*A+...+lambda_k*A for arbitrary integers lambda_1,...,lambda_k and integer sets A. We also establish an upper bound for such sums, which is similar to, but often stronger than Plunnecke's inequality.

14 pages, typos and small errors fixed