A Quantitative Result on Diophantine Approximation for Intersective Polynomials

Neil Lyall, Alex Rice

Published 2014-04-21Version 1

In this short note, we closely follow the approach of Green and Tao to extend the best known bound for recurrence modulo 1 from squares to the largest possible class of polynomials. The paper concludes with a brief discussion of a consequence of this result for polynomials structures in sumsets and limitations of the method.