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ON IRREGULARITIES OF DISTRIBUTION II

Published online by Cambridge University Press:  01 February 1999

R. C. BAKER
R. C. BAKER
Affiliation:
Department of Mathematics, Brigham Young University, Provo, UT 84602, USA
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Abstract

Let a=(a1, a2, a3, …) be an arbitrary infinite sequence in U=[0, 1). Let

formula here

Van der Corput [5] conjectured that d(a, n) (n=1, 2, …) is unbounded, and this was proved in 1945 by van Aardenne-Ehrenfest [1]. Later she refined this [2], obtaining

formula here

for infinitely many n. Here and later c1, c2, … denote positive absolute constants.

In 1954, Roth [8] showed that the quantity

formula here

is closely related to the discrepancy of a suitable point set in U2.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 50 - 64
Copyright
The London Mathematical Society 1999

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