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

Mordechay Levin; Meir Smorodinsky

Colloquium Mathematicae (2000)

  • Volume: 84/85, Issue: 2, page 431-441
  • ISSN: 0010-1354

Abstract

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

How to cite

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Levin, Mordechay, and Smorodinsky, Meir. "A $ℤ^{d}$ generalization of the Davenport-Erdős construction of normal numbers." Colloquium Mathematicae 84/85.2 (2000): 431-441. <http://eudml.org/doc/210824>.

@article{Levin2000,
abstract = {We extend the Davenport and Erdős construction of normal numbers to the $ℤ^\{d\}$ case.},
author = {Levin, Mordechay, Smorodinsky, Meir},
journal = {Colloquium Mathematicae},
keywords = {uniform distribution of sequences; normal numbers; discrepancy; rectangular normal; asymptotic frequency; estimates of exponential sums; Erdős-Turán inequality},
language = {eng},
number = {2},
pages = {431-441},
title = {A $ℤ^\{d\}$ generalization of the Davenport-Erdős construction of normal numbers},
url = {http://eudml.org/doc/210824},
volume = {84/85},
year = {2000},
}

TY - JOUR
AU - Levin, Mordechay
AU - Smorodinsky, Meir
TI - A $ℤ^{d}$ generalization of the Davenport-Erdős construction of normal numbers
JO - Colloquium Mathematicae
PY - 2000
VL - 84/85
IS - 2
SP - 431
EP - 441
AB - We extend the Davenport and Erdős construction of normal numbers to the $ℤ^{d}$ case.
LA - eng
KW - uniform distribution of sequences; normal numbers; discrepancy; rectangular normal; asymptotic frequency; estimates of exponential sums; Erdős-Turán inequality
UR - http://eudml.org/doc/210824
ER -

References

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  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. Zbl0448.10050
  2. [B] E. Borel, Les probabilités dénombrables et leurs applications arithmétiques, Rend. Circ. Mat. Palermo 27 (1909), 247-271. Zbl40.0283.01
  3. [C] D. J. Champernowne, The construction of decimals normal in the scale ten, J. London Math. Soc. 8 (1933), 254-260. Zbl0007.33701
  4. [Ci] J. Cigler, Asymptotische Verteilung reeller Zahlen mod 1, Monatsh. Math. 64 (1960), 201-225. Zbl0111.25301
  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. Zbl0478.10036
  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. Zbl0643.10041

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