An inverse theorem for the Gowers U^(s+1)[N]-norm
نویسندگان
چکیده
منابع مشابه
5 an Inverse Theorem for the Gowers U 3 ( G ) Norm
There has been much recent progress in the study of arithmetic progressions in various sets, such as dense subsets of the integers or of the primes. One key tool in these developments has been the sequence of Gowers uniformity norms U d (G), d = 1, 2, 3,. .. on a finite additive group G; in particular, to detect arithmetic progressions of length k in G it is important to know under what circums...
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There has been much recent progress in the study of arithmetic progressions in various sets, such as dense subsets of the integers or of the primes. One key tool in these developments has been the sequence of Gowers uniformity norms U d (G), d = 1, 2, 3,. .. on a finite additive group G; in particular, to detect arithmetic progressions of length k in G it is important to know under what circums...
متن کاملA ug 2 00 6 AN INVERSE THEOREM FOR THE GOWERS U 3 ( G ) NORM
There has been much recent progress in the study of arithmetic progressions in various sets, such as dense subsets of the integers or of the primes. One key tool in these developments has been the sequence of Gowers uniformity norms U d (G), d = 1, 2, 3,. .. on a finite additive group G; in particular, to detect arithmetic progressions of length k in G it is important to know under what circums...
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We briefly discuss here the Balog-Szemerédi theorem, compare its different versions and prove, following Gowers, the strongest one — also due to Gowers. 1. Discussion For a finite set A of elements of an abelian group and a group element s, by νA(s) we denote the number of representations of s as a sum of two elements of A: νA(s) = #{(a′, a′′) ∈ A× A : s = a′ + a′′}. We write 2A = {a′ + a′′ : a...
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Let p be a fixed prime number, and N be a large integer. The ’Inverse Conjecture for the Gowers norm’ states that if the ”d-th Gowers norm” of a function f : Fp → F is non-negligible, that is larger than a constant independent of N , then f can be non-trivially approximated by a degree d − 1 polynomial. The conjecture is known to hold for d = 2, 3 and for any prime p. In this paper we show the ...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2012
ISSN: 0003-486X
DOI: 10.4007/annals.2012.176.2.11