Abstract
For given positive integer n and ε > 0 we consider an arbitrary nonempty subset A of a field consisting of p 2 elements such that its cardinality exceeds p 2/n−ε. We study the possibility to represent an arbitrary element of the field as a sum of at most N(n, ε) elements from the nth degree of the set A. An upper estimate for the number N(n, ε) is obtained when it is possible.
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References
A. Glibichuk and S. Konyagin, “Additive Properties of Product Sets in Fields of Prime Order,” Additive Combinatorics. Centre de Recherches Mathématiques. Proceedings and Notes 43, 279 (2007).
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Original Russian Text © A.A. Glibichuk, 2009, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2009, Vol. 64, No. 1, pp. 3–8.
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Glibichuk, A.A. Additive properties of product sets in the field \( \mathbb{F}_{p^2 } \) . Moscow Univ. Math. Bull. 64, 1–6 (2009). https://doi.org/10.3103/S002713220901001X
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DOI: https://doi.org/10.3103/S002713220901001X