Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-27T04:12:51.410Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)