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

Takahiko Fujita; Hiroshi Kaneko; Shin Matsumoto

doi:10.1515/MCMA.2008.013

Published by De Gruyter November 28, 2008

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

Takahiko Fujita , Hiroshi Kaneko and Shin Matsumoto

From the journal Monte Carlo Methods and Applications

https://doi.org/10.1515/MCMA.2008.013

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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.

Keywords.: Uniformly distributed; law of the iterated logarithm sequence

Received: 2008-05-24

Revised: 2008-10-06

Published Online: 2008-11-28

Published in Print: 2008-November

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

Abstract

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