Automation and Remote Control

, Volume 74, Issue 10, pp 1607–1613 | Cite as

Statistical properties of the Moebius function

  • Ya. G. Sinai
Topical Issue


Remote Control Limit Theorem Number Theory Zeta Function Gibbs Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Kac, M., Slatistical Independence in Probability, Analysis and Number Theory, New York: Wiley, 1959. Translated under the title Statisticheskaya nezavisimost’ v teorii veroyatnostei, analize i teorii chisel, Moscow: Inostrannaya Literatura, 1963.Google Scholar
  2. 2.
    Cellarosi, F. and Sinai, Ya.G., Ergodic Properties of Square-Free Numbers, J. Eur. Math. Soc., 2012 (also available at arXiv:1112.4691 [math.DS]).Google Scholar
  3. 3.
    Mirsky, L., Arithmetical Pattern Problems Relating to Divisibility by rth Powers, Proc. London Math. Soc., Ser. 2, 1949, vol. 50, pp. 497–508.MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Tsang, K., The Distribution of r-tuples of Squarefree Numbers, Mat., 1985, vol. 32, no. 2, pp. 265–275.MathSciNetMATHGoogle Scholar
  5. 5.
    Hall, R., The Distribution of Squarefree Numbers, J. Reine Angew. Math., 1989, vol. 394, pp. 107–117.MathSciNetMATHGoogle Scholar
  6. 6.
    von Neumann, J., Zur Operatorenmethode in der klassischen Mechanik, Ann. Math., 1932, vol. 33, pp. 587–642.CrossRefGoogle Scholar
  7. 7.
    von Neumann, J. and Halmos, P., Operator Methods in Classical Mechanics. II, Ann. Math., 1942, vol. 43, pp. 332–350.CrossRefMATHGoogle Scholar
  8. 8.
    Cellarosi, F. and Sinai, Ya.G., Non-Standard Limit Theorems in Number Theory, in Prokhorov and Contemporary Probability Theory, New York: Springer, 2013, vol. 33, pp. 197–214 (also available at arXiv:1010.0035 [math.PR]).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • Ya. G. Sinai
    • 1
  1. 1.Institute for Information Transmission Problems (Kharkevich Institute)Russian Academy of SciencesMoscowRussia

Personalised recommendations