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Optimal bound for the discrepancies of lacunary sequences

Volume 158 / 2013

Christoph Aistleitner, Katusi Fukuyama, Yukako Furuya Acta Arithmetica 158 (2013), 229-243 MSC: Primary 11A25; Secondary 60F15, 60G50. DOI: 10.4064/aa158-3-3

Abstract

The law of the iterated logarithm for discrepancies of lacunary sequences is studied. An optimal bound is given under a very mild Diophantine type condition.

Authors

  • Christoph AistleitnerInstitute of Mathematics A
    Graz University of Technology
    Steyrergasse 30
    8010 Graz, Austria
    e-mail
  • Katusi FukuyamaDepartment of Mathematics
    Kobe University
    Rokko, Kobe, 657-8501 Japan
    e-mail
  • Yukako FuruyaDepartment of Mathematics
    Kobe University
    Rokko, Kobe, 657-8501 Japan
    e-mail

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