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Additive Properties of Slowly Increasing Convex Sets

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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.

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Funding

This research was supported by the grant of the Russian Government, no. 075-15-2019-1926.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), 141701, Dolgoprudnyi, Russia

    K. I. Olmezov

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  1. K. I. Olmezov
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Correspondence to K. I. Olmezov.

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Olmezov, K.I. Additive Properties of Slowly Increasing Convex Sets. Math Notes 108, 827–841 (2020). https://doi.org/10.1134/S0001434620110255

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  • DOI: https://doi.org/10.1134/S0001434620110255

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