A short proof of a known result about the density of a certain set in\n [0,1]ⁿ

2014/10/14 by Dimitri Dias, Dias, Dimitri
Mathematics · #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1410.3894

openalex publication_date 2014/10/14 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In Theorem 1 of Acta Arith. 99 (2001), 321-329, Cobeli and Zaharescu give a\nresult about the distribution of the bf F_p-points on an affine curve. An\neasy corollary to their theorem is that the set bigcup_p lbrace\n(\(x₁)/(p), ...,\(x_n)/(p)), 1 \≤ x_i < p \and \∏_{1 \≤ i\n\≤ n} x_i \≡ 1 bmodp rbrace is dense in [ 0,1 ]ⁿ. In Integers 7\n(2007), A7, Foo gives a elementary proof of that fact in dimension 2.\nFollowing Foo's ideas, we give a similar proof in dimension greater than or\nequal to 3.\n

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