Metric Discrepancy Results for Sequences {nkx} and Diophantine Equations

  • István Berkes
  • Walter Philipp
  • Robert F. Tichy
Part of the Developments in Mathematics book series (DEVM, volume 16)


Let (n k ) be an increasing sequence of positive integers. For 0 ≤ x ≤ 1, set
$$ \eta _k = \eta _k \left( x \right): = n_k x \left( {mod 1} \right). $$


Discrepancy lacunary sequences Diophantine equations law of iterated algorithm 

2000 Mathematics subject classification

11K38 11D45 42A55 60F15 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • István Berkes
    • 1
  • Walter Philipp
    • 2
  • Robert F. Tichy
    • 3
  1. 1.Institut für Mathematik ATechnische Universität GrazGrazAustria
  2. 2.Institut für StatistikTechnische Universität GrazGrazAustria
  3. 3.Department of StatisticsUniversity of Illinois at Urbana-ChampaignChampaignUSA

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