Convexity and a sum-product type estimate

DOI10.4064/aa156-3-3zbMath1279.11013arXiv1111.5159OpenAlexW1992758844MaRDI QIDQ3144047

Liangpan Li, Oliver Roche-Newton

Publication date: 6 December 2012

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.5159

zbMATH Keywords

convex setssumsetssum-productsdoubling constants

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (19)

On the number of unit-area triangles spanned by convex grids in the plane ⋮ On sums of Szemerédi-Trotter sets ⋮ On sum sets and convex functions ⋮ On Distinct Consecutive Differences ⋮ Sumsets of semiconvex sets ⋮ Higher convexity and iterated second moment estimates ⋮ Some new results on higher energies ⋮ On the Minkowski distances and products of sum sets ⋮ Variations on the Sum-Product Problem II ⋮ An improved incidence bound for fields of prime order ⋮ On the few products, many sums problem ⋮ Few distinct distances implies no heavy lines or circles ⋮ New results for the growth of sets of real numbers ⋮ Some remarks on sets with small quotient set ⋮ On discrete values of bilinear forms ⋮ On higher energy decompositions and the sum–product phenomenon ⋮ Variations on the Sum-Product Problem ⋮ Sets with few distinct distances do not have heavy lines ⋮ New sum-product type estimates over finite fields

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