A slight improvement to Garaev's sum product estimate
نویسندگان
چکیده
منابع مشابه
M ar 2 00 7 A SLIGHT IMPROVEMENT TO GARAEV ’ S SUM PRODUCT ESTIMATE
Let A be a subset of F p , the field of p elements with p prime. We let A + A = {a + b : a ∈ A, b ∈ A}, and AA = {ab : a ∈ A, b ∈ A}. It is fun (and useful) to prove lower bounds on max(|A+A|, |AA|) (see e.g. [BKT],[BGK],[G]). Recently, Garaev [G] showed that when |A| < p 1 2 one has the estimate max(|A + A|, |AA|) |A| 15 14. By using Plunneke's inequality in a slightly more sophisticated way, ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09385-4