Proceedings of Integers Conference 2009 SUM - PRODUCT INEQUALITIES WITH PERTURBATION
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چکیده
Let A be a set of n > n0(ε) positive real numbers, all at least 1 apart. We show that, if δa,b and δ� a,b are arbitrary real numbers satisfying |δa,b| < n 1−ε a , and |δ � a,b| < n1−ε b , we have |{(a + δa,b)(b + δ� a,b) : a, b ∈ A}| + |A + A| � n1+ε/9 log n . – Dedicated to Mel Nathanson and Carl Pomerance on the occasion of their 65th birthdays
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