Sum - Product Estimates
نویسنده
چکیده
Notes on the sum-product estimates of Bourgain-Katz-Tao and BourgainKonyagin.
منابع مشابه
Sum-products Estimates with Several Sets and Applications
We obtain several versions of the sum-product theorem with k-fold sums and product sets. We also give several applications of these estimates.
متن کاملSlightly Improved Sum-product Estimates in Fields of Prime Order
Let Fp be the field of residue classes modulo a prime number p and let A be a nonempty subset of Fp. In this paper we show that if |A| p , then max{|A ± A|, |AA|} |A|; if |A| p, then max{|A ± A|, |AA|} v min{|A|( |A| p0.5 ), |A|( p |A| )}. These results slightly improve the estimates of Bourgain-Garaev and Shen. Sum-product estimates on different sets are also considered.
متن کاملNew Sum-product Type Estimates over Finite Fields
Let F be a field with positive odd characteristic p. We prove a variety of new sum-product type estimates over F . They are derived from the theorem that the number of incidences between m points and n planes in the projective three-space PG(3, F ), with m ≥ n = O(p), is O(m √ n+ km), where k denotes the maximum number of collinear planes. The main result is a significant improvement of the sta...
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We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.
متن کاملSum-product Estimates in Finite Fields via Kloosterman Sums
We establish improved sum-product bounds in finite fields using incidence theorems based on bounds for classical Kloosterman and related sums.
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