Polynomial Configurations in Difference Sets (Revised Version)
Classical Analysis and ODEs
2010-10-27 v3 Number Theory
Abstract
We prove a quantitative version of the Polynomial Szemeredi Theorem for difference sets. This result is achieved by first establishing a higher dimensional analogue of a theorem of Sarkozy (the simplest non-trivial case of the Polynomial Szemeredi Theorem asserting that the difference set of any subset of the integers of positive upper density necessarily contains a perfect square) and then applying a simple lifting argument.
Cite
@article{arxiv.0903.4504,
title = {Polynomial Configurations in Difference Sets (Revised Version)},
author = {Neil Lyall and Akos Magyar},
journal= {arXiv preprint arXiv:0903.4504},
year = {2010}
}
Comments
small corrections made