On theorems of Wirsing and Sanders
Volume 189 / 2019
Acta Arithmetica 189 (2019), 381-390
MSC: Primary 11B30; Secondary 11B05.
DOI: 10.4064/aa180125-20-9
Published online: 3 June 2019
Abstract
We generalize an argument of Wirsing to vector spaces over finite fields, giving a quantitative bound for the size of the sumset of an arbitrary set $A$ and a basis of the space. Then we use it to give a simpler proof of a result of Sanders on the existence of subspaces in the difference set $A-A$, where $A$ has density near $1/2$.
