Convexity and a sum-product type estimate
نویسندگان
چکیده
منابع مشابه
An explicit sum-product estimate in Fp
Let Fp be the field of residue classes modulo a prime number p and let A be a non-empty subset of Fp. In this paper we give an explicit version of the sum-product estimate of Bourgain, Katz, Tao and Bourgain, Glibichuk, Konyagin on the size of max{|A+A|, |AA|}. In particular, our result implies that if 1 < |A| ≤ p7/13(log p)−4/13, then max{|A + A|, |AA|} ≫ |A|15/14 (log |A|)2/7 . 2000 Mathemati...
متن کاملSzemerédi-Trotter type theorem and sum-product estimate in finite fields
We study a Szemerédi-Trotter type theorem in finite fields. We then use this theorem to obtain an improved sum-product estimate in finite fields.
متن کاملThe Sum-product Estimate for Large Subsets of Prime Fields
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|.
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چکیده ندارد.
Sum of Squares and Polynomial Convexity
The notion of sos-convexity has recently been proposed as a tractable sufficient condition for convexity of polynomials based on sum of squares decomposition. A multivariate polynomial p(x) = p(x1, . . . , xn) is said to be sos-convex if its Hessian H(x) can be factored as H(x) = M (x) M (x) with a possibly nonsquare polynomial matrix M(x). It turns out that one can reduce the problem of decidi...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2012
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa156-3-3