A Quantitative Result on Diophantine Approximation for Intersective   Polynomials
  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. 
Neil Lyall, Alex Rice
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