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Expanding Polynomials on Sets with Few Products

Pohoata, Cosmin (2020) Expanding Polynomials on Sets with Few Products. Mathematika, 66 (1). pp. 71-78. ISSN 0025-5793 . https://resolver.caltech.edu/CaltechAUTHORS:20191126-112419020

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Abstract

In this note, we prove that if A is a finite set of real numbers such that |AA|=K|A|, then for every polynomial f∈R[x,y] we have that |f(A,A)|=Ω_(K,degf)(|A|²), unless f is of the form f(x,y)=g(M(x,y)) for some monomial M and some univariate polynomial g. This is sharp up to the dependence on K and the degree of f.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1112/mtk.12007DOIArticle
https://arxiv.org/abs/1905.03456arXivDiscussion Paper
Additional Information:© 2019 The Author(s). The publishing rights for this article are licensed to University College London under an exclusive licence. Issue Online: 26 November 2019; Version of Record online: 26 November 2019; Manuscript received: 28 April 2019. I would like to thank Vlad Matei, Adam Sheffer and Dmitrii Zhelezov for useful discussions.
Issue or Number:1
Classification Code:MSC: 11B13; 11J87 (primary)
Record Number:CaltechAUTHORS:20191126-112419020
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191126-112419020
Official Citation:Pohoata, C. (2020), EXPANDING POLYNOMIALS ON SETS WITH FEW PRODUCTS. Mathematika, 66: 71-78. doi:10.1112/mtk.12007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100066
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Nov 2019 23:33
Last Modified:26 Nov 2019 23:33

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