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On Sequences {ξtn(mod 1)}

Published online by Cambridge University Press:  20 November 2018

E. Strzelecki
E. Strzelecki*
Affiliation:
University of Alberta, Alberta, Canada
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J. Mycielski has conveyed to me the following problem by P. Erdös. Let {tn} be a sequence of natural numbers such that

(a) Does there exist an irrational number η such that the sequence {tnη (mod 1)} is not dense in [0,1)?

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975 , pp. 727 - 738
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Erd?s, P. and Taylor, S.J., On the set of points on convergence of a lucunary trigonometric series and the equidistribution properties of related sequences, Proc. London Math. Soc. (3) 7 (1957), 598-615.Google Scholar
2. Strzelecki, E., On a problem of interpolation by periodic and almost periodic functions, Colloquium Mathematicum 11 (1963), 91-99.Google Scholar