On a result of Mahler on the decimal expansions of (nα)

Daniel Berend; Michael D. Boshernitzan

Acta Arithmetica (1994)

  • Volume: 66, Issue: 4, page 315-322
  • ISSN: 0065-1036

How to cite

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Daniel Berend, and Michael D. Boshernitzan. "On a result of Mahler on the decimal expansions of (nα)." Acta Arithmetica 66.4 (1994): 315-322. <http://eudml.org/doc/206608>.

@article{DanielBerend1994,
author = {Daniel Berend, Michael D. Boshernitzan},
journal = {Acta Arithmetica},
keywords = {-adic expansion; Kronecker sequence},
language = {eng},
number = {4},
pages = {315-322},
title = {On a result of Mahler on the decimal expansions of (nα)},
url = {http://eudml.org/doc/206608},
volume = {66},
year = {1994},
}

TY - JOUR
AU - Daniel Berend
AU - Michael D. Boshernitzan
TI - On a result of Mahler on the decimal expansions of (nα)
JO - Acta Arithmetica
PY - 1994
VL - 66
IS - 4
SP - 315
EP - 322
LA - eng
KW - -adic expansion; Kronecker sequence
UR - http://eudml.org/doc/206608
ER -

References

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  1. [AP] N. Alon and Y. Peres, Uniform dilations, J. Geom. Funct. Anal. 2 (1992), 1-28. 
  2. [B] M. Boshernitzan, Uniform distribution and Hardy fields, J. Analyse Math., to appear. Zbl0804.11046
  3. [C] J. R. Chen, On Professor Hua's estimate of exponential sums , Sci. Sinica 20 (1977), 711-719. Zbl0374.10024
  4. [G] S. Glasner, Almost periodic sets and measures on the torus, Israel J. Math. 32 (1979), 161-172. Zbl0406.54023
  5. [H] L. K. Hua, Introduction to Number Theory, Springer, New York, 1982. 
  6. [KN] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974. Zbl0281.10001
  7. [M] K. Mahler, Arithmetical properties of the digits of the multiples of an irrational number, Bull. Austral. Math. Soc. 8 (1973), 191-203. Zbl0248.10024
  8. [S] S. B. Stečkin, An estimate of a complete rational trigonometric sum, Analytic Number Theory, Mathematical Analysis and their Applications, Trudy Mat. Inst. Steklov. 143 (1977), 188-207, 211; English transl.: Proc. Steklov Inst. Math. (1980), 201-220. 
  9. [W] H. Weyl, Über die Gleichverteilung von Zahlen mod. Eins, Math. Ann. 77 (1916), 313-352. Zbl46.0278.06

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