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15 June 2002 A polynomial bound in Freiman's theorem
Mei-Chu Chang
Duke Math. J. 113(3): 399-419 (15 June 2002). DOI: 10.1215/S0012-7094-02-11331-3

Abstract

In this paper the following improvement on Freiman's theorem on set addition is obtained (see Theorems 1 and 2 in Section 1).

Let A be a finite set such that | A+A |<α| A | . Then A is contained in a proper d-dimensional progression P, where d[ α1 ] and log( | P |/| A | )<C α 2 ( logα ) 3 .

Earlier bounds involved exponential dependence in α in the second estimate. Our argument combines I. Ruzsa's method, which we improve in several places, as well as Y. Bilu's proof of Freiman's theorem.

Citation

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Mei-Chu Chang. "A polynomial bound in Freiman's theorem." Duke Math. J. 113 (3) 399 - 419, 15 June 2002. https://doi.org/10.1215/S0012-7094-02-11331-3

Information

Published: 15 June 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1035.11048
MathSciNet: MR1909605
Digital Object Identifier: 10.1215/S0012-7094-02-11331-3

Subjects:
Primary: 11P70
Secondary: 11B13, 11B25

Rights: Copyright © 2002 Duke University Press

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Vol.113 • No. 3 • 15 June 2002
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