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A uniformly distributed sequence on the ring of p-adic integers

Author

Listed:
  • Fujita Takahiko

    (Graduate School of Commerce and Management, Hitotsubashi University, Kunitachi, Tokyo, 186-8601, Japan. Email: fujita@math.hit-u.ac.jp)

  • Kaneko Hiroshi

    (Department of Mathematics, Tokyo University of Science, 26 Wakamiya, Shinjuku, Tokyo, 162-0827, Japan. Email: stochos@rs.kagu.tus.ac.jp)

  • Matsumoto Shin

    (Department of Mathematics, Tokyo University of Science, 26 Wakamiya, Shinjuku, Tokyo, 162-0827, Japan.)

Abstract

This article will be started with a fundamental observation on consecutive non-negative integers. Based on the observation, we will demonstrate that the sequence of non-negative integers is regarded as a uniformly distributed sequence in the ring of the p-adic integers. As a result, the sequence provides us with a faster rate of convergence than the one obtained by simply applying law of the iterated logarithm.

Suggested Citation

  • Fujita Takahiko & Kaneko Hiroshi & Matsumoto Shin, 2008. "A uniformly distributed sequence on the ring of p-adic integers," Monte Carlo Methods and Applications, De Gruyter, vol. 14(4), pages 303-310, January.
    • Handle: RePEc:bpj:mcmeap:v:14:y:2008:i:4:p:303-310:n:2
    DOI: 10.1515/MCMA.2008.013
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