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Matematicheskie Zametki, 2020, Volume 108, Issue 6, Pages 851–867
DOI: https://doi.org/10.4213/mzm12707 (Mi mzm12707) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Additive Properties of Slowly Increasing Convex Sets

K. I. Olmezov

Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
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DOI: https://doi.org/10.4213/mzm12707
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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1926
This work was supported by the Government Grant of the Russian Federation no. 075-15-2019-1926.
Received: 22.02.2020
Revised: 28.03.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 6, Pages 827–841
DOI: https://doi.org/10.1134/S0001434620110255
Bibliographic databases:
Document Type: Article
UDC: 511.178
Language: Russian
Citation: K. I. Olmezov, “Additive Properties of Slowly Increasing Convex Sets”, Mat. Zametki, 108:6 (2020), 851–867; Math. Notes, 108:6 (2020), 827–841
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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