Uniform distribution of two-term recurrence sequences

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let (FORMULA PRESENTED), A, B be rational integers and for (FORMULA PRESENTED). The sequence (un) is clearly periodic modulo m and we say that (un) is uniformly distributed modulo m if for every 5, every residue modulo m occurs the same number of times in the sequence of residues (FORMULA PRESENTED), where N is the period of (un) modulo m. If (un) is uniformly distributed modulo m then m divides N, so we write N=mf. Several authors have characterized those m for which (un) is uniformly distributed modulo m. In fact in this paper we will show that a much stronger property holds when m = pk, p a prime. Namely, if (un) is uniformly distributed modulo pk with period pkf, then every residue modulo pk appears exactly once in the sequence (FORMULA PRESENTED), for every s. We also characterize those composite m for which this more stringent property holds.

Original languageEnglish (US)
Pages (from-to)37-45
Number of pages9
JournalTransactions of the American Mathematical Society
Volume301
Issue number1
DOIs
StatePublished - 1987

Fingerprint

Uniform distribution
Recurrence
Modulo
Composite materials
Term
Divides
Composite
Integer

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Uniform distribution of two-term recurrence sequences. / Velez, William Yslas.

In: Transactions of the American Mathematical Society, Vol. 301, No. 1, 1987, p. 37-45.

Research output: Contribution to journalArticle

@article{3e0e06f60146470994e4e1dc44e4739d,
title = "Uniform distribution of two-term recurrence sequences",
abstract = "Let (FORMULA PRESENTED), A, B be rational integers and for (FORMULA PRESENTED). The sequence (un) is clearly periodic modulo m and we say that (un) is uniformly distributed modulo m if for every 5, every residue modulo m occurs the same number of times in the sequence of residues (FORMULA PRESENTED), where N is the period of (un) modulo m. If (un) is uniformly distributed modulo m then m divides N, so we write N=mf. Several authors have characterized those m for which (un) is uniformly distributed modulo m. In fact in this paper we will show that a much stronger property holds when m = pk, p a prime. Namely, if (un) is uniformly distributed modulo pk with period pkf, then every residue modulo pk appears exactly once in the sequence (FORMULA PRESENTED), for every s. We also characterize those composite m for which this more stringent property holds.",
author = "Velez, {William Yslas}",
year = "1987",
doi = "10.1090/S0002-9947-1987-0879561-2",
language = "English (US)",
volume = "301",
pages = "37--45",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "1",

}

TY - JOUR

T1 - Uniform distribution of two-term recurrence sequences

AU - Velez, William Yslas

PY - 1987

Y1 - 1987

N2 - Let (FORMULA PRESENTED), A, B be rational integers and for (FORMULA PRESENTED). The sequence (un) is clearly periodic modulo m and we say that (un) is uniformly distributed modulo m if for every 5, every residue modulo m occurs the same number of times in the sequence of residues (FORMULA PRESENTED), where N is the period of (un) modulo m. If (un) is uniformly distributed modulo m then m divides N, so we write N=mf. Several authors have characterized those m for which (un) is uniformly distributed modulo m. In fact in this paper we will show that a much stronger property holds when m = pk, p a prime. Namely, if (un) is uniformly distributed modulo pk with period pkf, then every residue modulo pk appears exactly once in the sequence (FORMULA PRESENTED), for every s. We also characterize those composite m for which this more stringent property holds.

AB - Let (FORMULA PRESENTED), A, B be rational integers and for (FORMULA PRESENTED). The sequence (un) is clearly periodic modulo m and we say that (un) is uniformly distributed modulo m if for every 5, every residue modulo m occurs the same number of times in the sequence of residues (FORMULA PRESENTED), where N is the period of (un) modulo m. If (un) is uniformly distributed modulo m then m divides N, so we write N=mf. Several authors have characterized those m for which (un) is uniformly distributed modulo m. In fact in this paper we will show that a much stronger property holds when m = pk, p a prime. Namely, if (un) is uniformly distributed modulo pk with period pkf, then every residue modulo pk appears exactly once in the sequence (FORMULA PRESENTED), for every s. We also characterize those composite m for which this more stringent property holds.

UR - http://www.scopus.com/inward/record.url?scp=84967713025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84967713025&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1987-0879561-2

DO - 10.1090/S0002-9947-1987-0879561-2

M3 - Article

AN - SCOPUS:84967713025

VL - 301

SP - 37

EP - 45

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -