Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T07:51:58.474Z Has data issue: false hasContentIssue false
  • English
  • Français

IP-Sets on the Circle

Published online by Cambridge University Press:  20 November 2018

Daniel Berend
Daniel Berend*
Affiliation:
Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let P be an IP-set of integers namely for a certain sequence The main questions studied here are : (1) Under what conditions on (an) is Pα dense modulo 1 for every irrational α? (2) Under what conditions on (an) is Pα (considered as a sequence ordered in a way to be subsequently defined) uniformly distributed modulo 1 for every irrational α?

Keywords

11J7111K0611K26
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 4 , 01 August 1990 , pp. 575 - 589
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Berend, D., Actions of sets of integers on irrationals, Acta Arithmetica 48 (1987), 163–170.Google Scholar
2. Erdös, P. and Taylor, S.J., On the set of points of convergence of a lacunary trigonometric series and the equidistribution properties of related sequences, Proc. London Math. Soc. (3), 7 (1957), 598–615.Google Scholar
3. Furstenberg, H., Disjointness in ergodic theory, minimal sets, and a problem in diophantineapproximation, Math. Systems Theory 1 (1967), 1–9.Google Scholar
4. Furstenberg, H., Recurrence in Ergodic Theory and Combinational Number Theory, Princeton University Press, Princeton, New Jersey, 1981.Google Scholar
5. Kuipers, L. and Niederreiter, H., Uniform Distribution of Sequences, Wiley, New York, 1974.Google Scholar
6. Meyer, Y., Algebraic Numbers and Harmonic Analysis, North-Holland Publishing Company, Amsterdam-London, 1972.Google Scholar
7. Pisot, C., La répartition modulo 1 et le nombres algébriques, Annali di Pisa (2) 7 (1938), 205–248.Google Scholar
8. Schmidt, W.M., Small fractional parts of polynomials, Regional Conference Series in Mathematics, No. 32, 1977.Google Scholar
9. Weyl, H., Über die Gleichverteilung die Zahlen mod Eins, Math. Annalen 77 (1916), 313–352.Google Scholar