Variations on the Sum-Product Problem II

DOI10.1137/17M112316XzbMath1370.11022arXiv1703.09549OpenAlexW2141292457MaRDI QIDQ5351868

Oliver Roche-Newton, Ilya D. Shkredov, Brendan Murphy

Publication date: 31 August 2017

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.09549

zbMATH Keywords

discrete geometryexpandersadditive combinatoricssum-product estimates

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Erd?s problems and related topics of discrete geometry (52C10) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (10)

Expanders with superquadratic growth ⋮ An update on the sum-product problem ⋮ A family of four-variable expanders with quadratic growth ⋮ On the few products, many sums problem ⋮ On the size of the set AA+A ⋮ Group actions, the Mattila integral and applications ⋮ Four-variable expanders over the prime fields ⋮ New expander bounds from affine group energy ⋮ On higher energy decompositions and the sum–product phenomenon ⋮ Products of Differences over Arbitrary Finite Fields

Cites Work

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• A bound on the multiplicative energy of a sum set and extremal sum-product problems
• On sums of Szemerédi-Trotter sets
• On the Erdős distinct distances problem in the plane
• New results on sums and products in \(\mathbb{R}\)
• Bounding multiplicative energy by the sumset
• On sum sets of sets having small product set
• Sets with few distinct distances do not have heavy lines
• Some new results on higher energies
• On Sumsets of Convex Sets
• Convexity and a sum-product type estimate
• On the number of sums and products
• Variations on the Sum-Product Problem

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