Duke Mathematical Journal
- Duke Math. J.
- Volume 113, Number 3 (2002), 399-419.
A polynomial bound in Freiman's theorem
In this paper the following improvement on Freiman's theorem on set addition is obtained (see Theorems 1 and 2 in Section 1).
Let be a finite set such that . Then A is contained in a proper d-dimensional progression P, where and .
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.
Duke Math. J. Volume 113, Number 3 (2002), 399-419.
First available in Project Euclid: 18 June 2004
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 11P70: Inverse problems of additive number theory, including sumsets
Secondary: 11B13: Additive bases, including sumsets [See also 05B10] 11B25: Arithmetic progressions [See also 11N13]
Chang, Mei-Chu. A polynomial bound in Freiman's theorem. Duke Math. J. 113 (2002), no. 3, 399--419. doi:10.1215/S0012-7094-02-11331-3. https://projecteuclid.org/euclid.dmj/1087575313