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 | |||||||||
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| 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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