THE SUM-PRODUCT ESTIMATE FOR LARGE SUBSETS OF PRIME FIELDS

By Moubariz Z. Garaev. 2007

95 citations recorded by the source corpus.

Let Fp be the field of prime order p. It is known that for any integer N ∈ [1,p] one can construct a subset A C Fp with |A| = N such that max{|A + A|, |AA|} «p 1/2 |A| 1/2 . One of the results of the present paper implies that if A C Fp with |A| > p 2/3 , then max{|A + A|, |AA|}» p 1/2 |A| 1/2 .

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/33fe4ab6c2ac62b2123a6c80d50cbe50529a6caf

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

Citations in the corpus

Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdos-Falconer distance conjecture (2007, background): “See also [2], [4], [8], [7], [11], [14], [19], [20] and the references contained therein on recent progress related to this problem and its analogs.”
Sums and products in finite fields: an integral geometric viewpoint (2007, background): “See also [1], [3], [5], [ 4 ], [8], [10], [12], [13] and the references contained therein on recent progress related to this problem and its analogs.”
New sum-product type estimates over finite fields (2014, methodology): “, [6], [25] (in the latter paper exponential sums are hidden in Lemma 1 therein).”
On the concentration of points of polynomial maps and applications (2012, methodology): “ut Following exactly the argument of Garaev [6] and using the estimate of Lemma 5, we obtain the following result for large sets A ⊆ Fp.”
On the size of the set A(A + 1) (2008, background): “Theorem 2 can be compared with the following estimate from [7]:”