### Abstract

Let k be a positive integer and α be a real number, and for n = 1,2,... let e_{n} = +1 if the fractional part of n^{k}α is < 1/2, and e_{n} = -1 if it is ≥ 1/2. The pseudorandom properties of the sequence e1, e2,... are studied. As measures of pseudorandomness, the regularity of the distribution relative to arithmetic progressions and the correlation are used. In a previous paper the authors studied the special cases k = 1 and k = 2, while here the case k > 2 is considered.

Original language | English |
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Pages (from-to) | 281-298 |

Number of pages | 18 |

Journal | Monatshefte fur Mathematik |

Volume | 130 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 1 2000 |

### Keywords

- Binary sequence
- Pseudorandom
- Uniform distribution

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'On finite pseudorandom binary sequences, VI, (On (n<sup>k</sup>α) sequences)'. Together they form a unique fingerprint.

## Cite this

Mauduit, C., & Sárközy, A. (2000). On finite pseudorandom binary sequences, VI, (On (n

^{k}α) sequences).*Monatshefte fur Mathematik*,*130*(4), 281-298. https://doi.org/10.1007/s006050070028