Jean Bourgain

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math.CO2003

On the size of $k$ -fold sum and product sets of integers

Jean Bourgain, Mei-Chu Chang

We prove the following theorem: for all positive integers $b$ there exists a positive integer $k$ , such that for every finite set $A$ of integers with cardinality $∣ A ∣ > 1$ , we hav…

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…

On the size of k-fold sum and product sets of integers

A sum-product estimate in finite fields, and applications

On the size of $k$ -fold sum and product sets of integers