On large subsets of \mathbb F_q^n with no three-term arithmetic progression
نویسندگان
چکیده
منابع مشابه
On subsets of abelian groups with no 3-term arithmetic progression
A short proof of the following result of Brown and Buhler is given: For any E > 0 there exists n, = no(E) such that if A is an abelian group of odd order IAl > no and BG A with IBI >&IAI. then B must contain three distinct elements X, y, z satisfying x + y = 22.
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Let G ' Z/k1Z⊕ · · · ⊕ Z/kNZ be a finite abelian group with ki|ki−1 (2 ≤ i ≤ N). For a matrix Y = ( ai,j ) ∈ ZR×S satisfying ai,1 + · · ·+ ai,S = 0 (1 ≤ i ≤ R), let DY (G) denote the maximal cardinality of a set A ⊆ G for which the equations ai,1x1 + · · · + ai,SxS = 0 (1 ≤ i ≤ R) are never satisfied simultaneously by distinct elements x1, . . . , xS ∈ A. Under certain assumptions on Y and G, w...
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Suppose that f : Fpn → [0, 1] satisfies Σaf(m) = θF ∈ [F , F ], where F = |Fpn | = p. In this paper we will show the following: Let fj denote the size of the jth largest Fourier coefficient of f . If fj < θ j1/2+δF, for some integer j satisfying J0(δ, p) < j < F , then S = support(f) contains a non-trivial three-term arithmetic progression. Thus, the result is asserting that if the Fourier tran...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2017
ISSN: 0003-486X
DOI: 10.4007/annals.2017.185.1.8