This article is cited in 2 papers

Additive Properties of Slowly Increasing Convex Sets

K. I. Olmezov

Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region

Abstract: We obtain new estimates for the distribution of convolutions of the set of values of a convex function at integer points under additional conditions on the higher derivatives of the function. New estimates for additive energy and for the dimension of sumsets and sets of differences of such sets arise as natural consequences.

Keywords: additive combinatorics, additive energy, sumsets, convex sets, convex sequences.

UDC: 511.178

Received: 22.02.2020
Revised: 28.03.2020

DOI: 10.4213/mzm12707

 English version: Mathematical Notes, 2020, 108:6, 827–841

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