Geodesic
Additive Properties of Slowly Increasing Convex Sets
Matematičeskie zametki, Tome 108 (2020) no. 6, pp. 851-867

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2020_108_6_a3,
     author = {K. I. Olmezov},
     title = {Additive {Properties} of {Slowly} {Increasing} {Convex} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {851--867},
     publisher = {mathdoc},
     volume = {108},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_108_6_a3/}
}
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K. I. Olmezov. Additive Properties of Slowly Increasing Convex Sets. Matematičeskie zametki, Tome 108 (2020) no. 6, pp. 851-867. http://geodesic.mathdoc.fr/item/MZM_2020_108_6_a3/