On Additive Bases of Sets with Small Product Set

DOI10.1093/imrn/rnw291zbMath1448.11024arXiv1606.02320OpenAlexW2963588150MaRDI QIDQ4619342

Ilya D. Shkredov, Dmitrii Zhelezov

Publication date: 6 February 2019

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.02320

zbMATH Keywords

additive basessum-products

Mathematics Subject Classification ID

Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Additive bases, including sumsets (11B13)

Related Items (8)

If \(A + A\) is small then \(AAA\) is superquadratic ⋮ Expanders with superquadratic growth ⋮ An application of the sum-product phenomenon to sets avoiding several linear equations ⋮ On sums and products of combinatorial cubes ⋮ On the few products, many sums problem ⋮ NEW RESULTS ON SUM‐PRODUCT TYPE GROWTH OVER FIELDS ⋮ On asymptotic formulae in some sum–product questions ⋮ Any small multiplicative subgroup is not a sumset

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