Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2025-01-05T16:22:57.779Z Has data issue: false hasContentIssue false
  • English
  • Français

Results on fractional parts of linear functions of n and applications to Beatty sequences

Published online by Cambridge University Press:  17 April 2009

Takao Komatsu
Takao Komatsu
Affiliation:
School of Mathematics, Physics, Computing and Electronics, Macquarie University, New South Wales 2109, Australia, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Abstracts of Australasian Ph.D. Theses
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 349 - 351
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Borwein, J.M. and Borwein, P.B., ‘On the generating functions of the integer part: [nα+ γ]’, J. Number Theory 43 (1993), 293–318.CrossRefGoogle Scholar
[2]Fraenkel, A.S., Mushkin, M. and Tassa, U., ‘Determination of [nθ] by its sequence of differences’, Canad. Math. Bull. 21 (1978), 441–446.CrossRefGoogle Scholar
[3]Komatsu, T., ‘On the characteristic word of the inhomogeneous Beatty sequence’, Bull. Austral. Math. Soc. 51 (1995), 337–351.CrossRefGoogle Scholar
[4]Komatsu, T., ‘The fractional part of nθ+ø and Beatty sequences’, J. Théorie des Nombres de Bordeaux (to appear).Google Scholar
[5]Nishioka, K., Shiokawa, I. and Tamura, J., ‘Arithmetical properties of a certain power series’, J. Number Theory 42 (1992), 61–87.CrossRefGoogle Scholar
[6]van Ravenstein, T., ‘The three gap theorem (Steinhaus conjecture)’, J. Austral. Math. Soc. Ser. A 45 (1988), 360–370.CrossRefGoogle Scholar
[7]Venkov, B.A., Elementary number theory (Wolters-Noordhoff, Groningen, 1970).Google Scholar