A robust version of Freiman's 3k-4 Theorem and applications

Xuancheng Shao; Wenqiang Xu

doi:10.1017/S0305004118000129

A robust version of Freiman's 3k-4 Theorem and applications

Xuancheng Shao, Wenqiang Xu

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove a robust version of Freiman's 3k - 4 theorem on the restricted sumset A+ΓB, which applies when the doubling constant is at most (3+)/2 in general and at most 3 in the special case when A = -B. As applications, we derive robust results with other types of assumptions on popular sums, and structure theorems for sets satisfying almost equalities in discrete and continuous versions of the Riesz-Sobolev inequality.

Original language	English
Pages (from-to)	567-581
Number of pages	15
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	166
Issue number	3
DOIs	https://doi.org/10.1017/S0305004118000129
State	Published - May 1 2019

Bibliographical note

Funding Information:
SHAO XUANCHENG † XU WENQIANG ‡ Department of Mathematics , 715 Patterson Office Tower , University of Kentucky , Lexington , KY , 40506 , U.S.A. e-mail: xuancheng.shao@uky.edu Department of Mathematics , University College London , Gower Street , London , WC1E 6BT . e-mail: wenqiang.xu@ucl.ac.uk † Supported by a Glasstone Research Fellowship. ‡ Supported by a London Mathematics Society Undergraduate Research Bursary and the Mathematical Institute at University of Oxford. 05 2019 27 03 2018 166 3 567 581 04 12 2017 20 02 2018 Copyright © Cambridge Philosophical Society 2018 2018 Cambridge Philosophical Society

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© Copyright Cambridge Philosophical Society 2018.

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Mathematics (all)

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A robust version of Freiman's 3k-4 Theorem and applications

Abstract

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