The Sum-product Estimate for Large Subsets of Prime Fields
نویسنده
چکیده
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 ⊂ Fp with |A| = N such that max{|A+ A|, |AA|} p|A|. One of the results of the present paper implies that if A ⊂ Fp with |A| > p2/3, then max{|A+ A|, |AA|} p|A|.
منابع مشابه
un 2 00 7 the sum - product estimate for large subsets of prime fields
Let F p be the field of a prime order p. It is known that for any integer N ∈ [1, p] one can construct a subset A ⊂ F p with |A| = N such that max{|A + A|, |AA|} ≪ p 1/2 |A| 1/2. In the present paper we prove that if A ⊂ F p with |A| > p 2/3 , then max{|A + A|, |AA|} ≫ p 1/2 |A| 1/2 .
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تاریخ انتشار 2008