### 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 |
---|---|

Pages (from-to) | 281-298 |

Number of pages | 18 |

Journal | Monatshefte fur Mathematik |

Volume | 130 |

Issue number | 4 |

Publication status | Published - 2000 |

### Fingerprint

### Keywords

- Binary sequence
- Pseudorandom
- Uniform distribution

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

^{k}α) sequences).

*Monatshefte fur Mathematik*,

*130*(4), 281-298.

**On finite pseudorandom binary sequences, VI, (On (n ^{k}α) sequences).** / Mauduit, Christian; Sárközy, A.

Research output: Contribution to journal › Article

^{k}α) sequences)',

*Monatshefte fur Mathematik*, vol. 130, no. 4, pp. 281-298.

^{k}α) sequences). Monatshefte fur Mathematik. 2000;130(4):281-298.

}

TY - JOUR

T1 - On finite pseudorandom binary sequences, VI, (On (nkα) sequences)

AU - Mauduit, Christian

AU - Sárközy, A.

PY - 2000

Y1 - 2000

N2 - Let k be a positive integer and α be a real number, and for n = 1,2,... let en = +1 if the fractional part of nkα is <1/2, and en = -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.

AB - Let k be a positive integer and α be a real number, and for n = 1,2,... let en = +1 if the fractional part of nkα is <1/2, and en = -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.

KW - Binary sequence

KW - Pseudorandom

KW - Uniform distribution

UR - http://www.scopus.com/inward/record.url?scp=0034366217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034366217&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0034366217

VL - 130

SP - 281

EP - 298

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 4

ER -