Equivalence of polynomial conjectures in additive combinatorics
نویسنده
چکیده
We study two conjectures in additive combinatorics. The first is the polynomial Freiman-Ruzsa conjecture, which relates to the structure of sets with small doubling. The second is the inverse Gowers conjecture for U3, which relates to functions which locally look like quadratics. In both cases a weak form, with exponential decay of parameters is known, and a strong form with only a polynomial loss of parameters is conjectured. Our main result is that the two conjectures are in fact equivalent.
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عنوان ژورنال:
- Combinatorica
دوره 32 شماره
صفحات -
تاریخ انتشار 2010