The inverse conjecture for the Gowers norm over finite fields via the correspondence principle
نویسندگان
چکیده
منابع مشابه
The Inverse Conjecture for the Gowers Norm over Finite Fields via the Correspondence Principle Terence Tao and Tamar Ziegler
The inverse conjecture for the Gowers norms U(V ) for finite-dimensional vector spaces V over a finite field F asserts, roughly speaking, that a bounded function f has large Gowers norm ‖f‖Ud(V ) if and only if it correlates with a phase polynomial φ = eF(P ) of degree at most d− 1, thus P : V → F is a polynomial of degree at most d− 1. In this paper, we develop a variant of the Furstenberg cor...
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15 صفحه اولA correspondence principle for the Gowers norms
Informally speaking, the Furstenberg Correspondence [5, 6] shows that the “local behavior” of a dynamical system is controlled by the behavior of sufficiently large finite systems. By the local behavior of a dynamical system (X,B, μ,G), we mean the properties which can be stated using finitely many actions of G and the integral given by μ1. By a finite system, we just mean (S,P(S), c, G) where ...
متن کامل2 1 N ov 2 00 7 Inverse Conjecture for the Gowers norm is false
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 ...
متن کاملN ov 2 00 7 Inverse Conjecture for the Gowers norm is false
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: Analysis & PDE
سال: 2010
ISSN: 1948-206X,2157-5045
DOI: 10.2140/apde.2010.3.1