Some new results on higher energies

I. D. Shkredov

Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 74 (2013) no. 1, pp. 35-73.

Résumé

This article is concerned with the method of higher energies from combinatorial number theory. Upper bounds are obtained for the additive energies of convex sets and of sets $A$ with small $|AA|$ and $|A(A+1)|$. New structural results, involving the notion of a dual popular difference set, are proved in terms of higher energies.

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