On Restricted Arithmetic Progressions over Finite Fields
نویسنده
چکیده
Let A be a subset of Fp , the n-dimensional linear space over the prime field Fp of size at least δN (N = p), and let Sv = P −1(v) be the level set of a homogeneous polynomial map P : Fp → Fp of degree d, for v ∈ Fp . We show, that under appropriate conditions, the set A contains at least cN |S| arithmetic progressions of length l ≤ d with common difference in Sv, where c is a positive constant depending on δ, l and P . We also show that the conditions are generic for a class of sparse algebraic sets of density ≈ N−γ .
منابع مشابه
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