Monatshefte für Mathematik

, Volume 103, Issue 3, pp 233–240 | Cite as

Some estimates of theH-uniform distribution

  • Peter Schatte


The sequences (y n )=(a+blogn n ) are uniformly distributed in the sense of the summation methodH. In the present paper the speed of convergence of this procedure is estimated for these, sequences and for some other sequences. For the sequences (a+blogn) theH-means converge considerably faster than logarithmic means.


Uniform Distribution 
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  1. [1]
    Hlawka, E.: Theorie der Gleichverteilung. Mannheim-Wien-Zürich: B.I. 1979.Google Scholar
  2. [2]
    Kuipers, L., Niederreiter, H.: Uniform Distribution of Sequences. New York: J. Wiley. 1974.Google Scholar
  3. [3]
    Nagasaka, K.: On Benford's law. Ann. Inst. Statist. Math.36, 337–352 (1984).Google Scholar
  4. [4]
    Schatte, P.: Zur Verteilung der Mantisse in der Gleitkommadarstellung einer Zufallsgröße. Z. Angew. Math. und Mech.53, 553–565 (1973).Google Scholar
  5. [5]
    Schatte, P.: DieH -Limitierbarkeit einer Klasse von Zahlenfolgen. Math. Nachr.60, 181–190 (1974).Google Scholar
  6. [6]
    Schatte, P.: Ein Kriterium für dieH -Limitierbarkeit. Math. Nachr.64, 63–70 (1974).Google Scholar
  7. [7]
    Schatte, P.: OnH -summability and the uniform distribution of sequences. Math. Nachr.113, 237–243 (1983).Google Scholar
  8. [8]
    Schatte, P.: On the asymptotic logarithmic distribution of the floating-point mantissas of sums. Math. Nachr.127, 7–20 (1986).Google Scholar
  9. [9]
    Schatte, P.: On the almost sure convergence of floating-point mantissas and Benford's law. Math. Nachr. To appear 1987.Google Scholar
  10. [10]
    Schatte, P.: The asymptotic behaviour of the mantissa distributions of sums. J. Inf. Process. Cybern. EIK23 (1987).Google Scholar
  11. [11]
    Tichy, R. F.: Uniform distribution and diophantine inequalities. Mh. Math.99, 147–152 (1985).Google Scholar
  12. [12]
    Tichy, R. F.: Gleichverteilung zum SummierungsverfahrenH . Math. Nachr. To appear 1987.Google Scholar
  13. [13]
    Zeller, K., Beekmann, W.: Theorie der Limitierungsverfahren. Berlin-Heidelberg-New York: Springer. 1970.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Peter Schatte
    • 1
  1. 1.Sektion Mathematik der Bergakademie FreibergFreibergGerman Democratic Republic

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