ArticleOriginal scientific text

Title

A d generalization of the Davenport-Erdős construction of normal numbers

Authors 1, 2

Affiliations

  1. Department of Mathematics and Computer Science, Bar-Ilan University, 52900 Ramat-Gan, Israel
  2. School of Mathematical Sciences, Tel Aviv University, 69978 Tel-Aviv, Israel

Abstract

We extend the Davenport and Erdős construction of normal numbers to the d case.

Bibliography

  1. [AKS] R. Adler, M. Keane and M. Smorodinsky, A construction of a normal number for the continued fraction transformation, J. Number Theory 13 (1981), 95-105.
  2. [B] E. Borel, Les probabilités dénombrables et leurs applications arithmétiques, Rend. Circ. Mat. Palermo 27 (1909), 247-271.
  3. [C] D. J. Champernowne, The construction of decimals normal in the scale ten, J. London Math. Soc. 8 (1933), 254-260.
  4. [Ci] J. Cigler, Asymptotische Verteilung reeller Zahlen mod 1, Monatsh. Math. 64 (1960), 201-225.
  5. [DE] H. Davenport and P. Erdős, Note on normal numbers, Canad. J. Math. 4 (1953), 58-63.
  6. [DrTi] M. Drmota and R. Tichy, Sequences, Discrepancies and Applications, Lecture Notes in Math. 1651, Springer, 1997.
  7. [KT] P. Kirschenhofer and R. F. Tichy, On uniform distribution of double sequences, Manuscripta Math. 35 (1981), 195-207.
  8. [LeSm] M. B. Levin and M. Smorodinsky, On explicit construction of normal lattices, preprint.
  9. [SW] M. Smorodinsky and B. Weiss, Normal sequences for Markov shifts and intrinsically ergodic subshifts, Israel J. Math. 59 (1987), 225-233.
Pages:
431-441
Main language of publication
English
Received
1999-08-27
Accepted
2000-02-17
Published
2000
Exact and natural sciences