On two-point configurations in subsets of pseudo-random sets
نویسنده
چکیده
We prove a transference type result for pseudo-random subsets of Z N that is analogous to the well-known Fürstenberg-Sárközy theorem. More precisely, let k 2 be an integer and let and be real numbers satisfying + ()/(2 k+1 3) > 1. Let ✓ Z N be a set with size at least N and linear bias at most N. Then, every A ✓ with relative density |A|/|| (log log N) 1 2 log log log log log N contains a pair of the form {x, x + d k } for some nonzero integer d. Our approach uses techniques of Green as seen in [6] relying on a Fourier restriction type result also due to Green.
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