Article contents
A metrical result on the discrepancy of (nα)
Published online by Cambridge University Press: 18 May 2009
Extract
In the following let Ω be the set of irrational numbers in the interval [0,1] and let λ be Lebesgue measure restricted to Ω. For any real number x, let {x} = x - [x] be the fractional part of x. Let N be anatural number and let α e Ω. Then
is known as the discrepancy of the sequence (nα)n>1 modulo 1; here c[x, y) denotes the characteristic function of the interval [x, y).
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 1998
References
REFERENCES
- 7
- Cited by