Combinational properties of sets of residues modulo a prime and the Erdős—Graham problem

By A. Glibichuk. 2006

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Additive properties of product sets in fields of prime order (2007, background): “In [4], by using combinatorial arguments, it has been proven that 8XY = Z p for any X ⊂ Z p , Y ⊂ Z p provided that |X||Y | > p and either Y = −Y , or Y ∩ (−Y ) = ∅.”
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.”
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.”