IJPAM: Volume 72, No. 4 (2011)

UNIFORM EQUIPARTITION TEST BOUNDS
FOR MULTIPLY SEQUENCES

Marco Pollanen
Department of Mathematics
Trent University
Peterborough, ON K9J 7B8, CANADA


Abstract. For almost all $x_0 \in [0,1)$, the multiply sequence $x_n = a x_{n-1} \mbox{ mod } 1$, with $a>1$ an integer, is equidistributed. In this paper we show that equidistributed multiply sequences are not $m$-equipartitioned for any $m>2$. We also provide uniform asymptotic bounds for equipartition tests for such sequences.

Received: July 6, 2011

AMS Subject Classification: 11K06, 11J71

Key Words and Phrases: multiply sequences, equipartition, $\infty$-distribution

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 4