N. Katz

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19992003

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math.CO2003

A sum-product estimate in finite fields, and applications

Jean Bourgain, Nets Katz, Terence Tao

Let $A$ be a subset of a finite field $F := Z / q Z$ for some prime $q$ . If $∣ F ∣^{δ} < ∣ A ∣ < ∣ F ∣^{1 - δ}$ for some $δ > 0$ , then we prove the estimate $|A+A| + |A.A| \geq c(δ) |A|^{1+\eps…

math.CO1999

A new bound on partial sum-sets and difference-sets, and applications to the Kakeya conjecture

Nets Hawk Katz, Terence Tao

Let $A, B$ , be finite subsets of an abelian group, and let $G \subset A \times B$ be such that $# A, # B, # \{a+b: (a,b) \in G \} \leq N$. We consider the question of estimating th…