On the pseudo-random properties of nc

Christian Mauduit, Joël Rivat, András Sárkozy

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Abstract

We estimate the well-distribution measure and correlation of order 2 of the binary sequence EN = {e1,..., eN} defined by en = +1 if 0 ≤ {nc} < 1/2 and en = -1 if 1/2 ≤ {nc} < 1, where c is a real, non-integral number greater than L and {x} denotes the fractional part of x. We also prove an upper bound for the well-distribution measure of an arbitrary binary sequence in terms of its generating function and show that there exists no upper bound of this type for the correlation. The proof is based on the Erdös-Turán inequality, which we establish with an improved constant.

Original languageEnglish
Pages (from-to)185-197
Number of pages13
JournalIllinois Journal of Mathematics
Volume46
Issue number1
Publication statusPublished - Mar 1 2002

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ASJC Scopus subject areas

  • Mathematics(all)

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