Published January 2020
| Submitted
Journal Article
Open
Expanding Polynomials on Sets with Few Products
- Creators
- Pohoata, Cosmin
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.
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.Attached Files
Submitted - 1905.03456.pdf
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1905.03456.pdf
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Additional details
- Eprint ID
- 100066
- Resolver ID
- CaltechAUTHORS:20191126-112419020
- Created
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2019-11-26Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field