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The fractional parts of a smooth sequence

Published online by Cambridge University Press:  26 February 2010

M. N. Huxley
M. N. Huxley
Affiliation:
School of Mathematics, University of Wales College Cardiff, Senghenydd Road, Cardiff, CF2 4AG
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Extract

One construction used to produce a random number table is to take a smooth function F(x) taking values between 0 and 1, to evaluate it at N points spaced 1/M apart, and to ignore the first t decimal digits. With T = 10t this corresponds to taking the fractional part of

where T>M>N. The grounds for assuming this sequence to be random are that it is so difficult to prove anything about it.

Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988 , pp. 292 - 296
Copyright
Copyright © University College London 1988

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References

1.Graham, S. W. and Kolesnik, G.. Van der Corput's Method for Exponential Sums, London Math. Soc. Lecture Notes (to appear).Google Scholar
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