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On Finite Pseudorandom Binary Sequences, V.On (nα) and (n 2α) Sequences

Abstract.

 Let k be a positive integer and α be a real number, and for if the fractional part of is <1/2 and e n =−1 if it is ≥1/2. The pseudorandom properties of the sequence are studied. As measures of pseudorandomness, the regularity of the distribution relative to arithmetic progressions and the correlation are used. Here the special cases k=1 and k=2 are studied (while the case k>2 will be studied in the sequel).

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(Received 23 April 1999)

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Mauduit, C., Sárközy, A. On Finite Pseudorandom Binary Sequences, V.On (nα) and (n 2α) Sequences. Mh Math 129, 197–216 (2000). https://doi.org/10.1007/s006050050071

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  • DOI: https://doi.org/10.1007/s006050050071

  • 1991 Mathematics Subject Classification: 11K45
  • Key words: Pseudorandom, correlation, uniform distribution, diophantine approximation