Additive properties of products of subsets of the set \mathbb{F}_{p^2} / A. A. Glibichuk, S. V. Konyagin. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. № 1. P. 3-8
[Moscow Univ. Math. Bulletin. Vol. 64,
N 1, 2009. P. 1-6].
For given positive integer nand \varepsilon>0 we consider an arbitrary nonempty subset A of a field consisting of p^2 elements such that its cardinality exceeds p^{\frac{2}{n-\varepsilon}}. We study the possibility to represent an arbitrary element of the field as a sum of at most N(n,\varepsilon) elements from the nth degree of the set A. An upper estimate for the number N(n,\varepsilon) is obtained when it is possible.
