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On uniform distribution of αβ-orbits.
- Source :
-
Journal of Number Theory . Feb2021, Vol. 219, p386-403. 18p. - Publication Year :
- 2021
-
Abstract
- Let α , β ∈ (0 , 1) such that at least one of them is irrational. We take a random walk on the real line such that the choice of α and β has equal probability 1/2. We prove that almost surely the αβ -orbit is uniformly distributed module one, and the exponential sums along its orbit have the square root cancellation. We also show that the exceptional set in the probability space, which does not have the property of uniform distribution modulo one, is large in the terms of topology and Hausdorff dimension. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FRACTAL dimensions
*SQUARE root
*RANDOM walks
*EXPONENTIAL sums
*TOPOLOGY
Subjects
Details
- Language :
- English
- ISSN :
- 0022314X
- Volume :
- 219
- Database :
- Academic Search Index
- Journal :
- Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 147117173
- Full Text :
- https://doi.org/10.1016/j.jnt.2020.08.011