Additive properties of product sets in fields of prime order

By Glibichuk A A, Konyagin S V. 2007

71 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/ea09d909aede742320e0632e227965e2d9419d75

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In Discrete Mathematics and Combinatorics

Citations in the corpus

Multilinear Exponential Sums in Prime Fields Under Optimal Entropy Condition on the Sources (2009, background): “Proof. What follows is a variant of an argument due to Glibichuk and Konyagin [ GK ].”
Averages over hyperplanes, sum-product theory in vector spaces over finite fields and the Erdos-Falconer distance conjecture (2007, background): “Glibichuk and Konyagin, [9], proved that if A is subgroup of Z∗p, and |A| > pδ, δ > 0, then NA = Zp with N ≥ C4 1δ .”
On the size of the set A(A + 1) (2008, unknown): “Due to the observation of Glibichuk and Konyagin [8], either A1 − A1 A1 − A1 = Fp or we can choose elements b1, b ′ 2, b ′ 3, b ′ 4 ∈ A1 such that b1 − b2 b3 − b4 − 1 6∈ A1 − A1 A1 − A1 .”
Pinned distance sets, k-simplices, Wolff’s exponent in finite fields and sum-product estimates (2009, background): “For example, Glibichuk and Konyagin, [14] (see also [12]), proved in the case of prime fields Zp that for ∣A∣ > √ p that on case take d = 8.”
An Explicit Sum-Product Estimate in p (2010, methodology): “The following lemma follows from the work of Glibichuk and Konyagin [ 8 ].”
Sums and products in finite fields: an integral geometric viewpoint (2007, background): “Also, Theorem 1.1 gives an explicit bound for the conjecture mentioned in [ 6 ], namely that if |A| C q”
On asymptotic formulae in some sum–product questions (2018, background): “Our paper is devoted to so–called the sum–product phenomenon in Fp which was developed in papers [1]–[17], [27]—[43], [48]—[53], [57], [58] and in many others.”
On a variant of sum-product estimates and explicit exponential sum bounds in prime fields (2009, methodology): “The proof of this lemma easily follows from the arguments of the work of Glibichuk and Konyagin [11].”