Martingale differences and the metric theory of continued fractions
Number Theory
2009-07-01 v1 Probability
Abstract
We investigate a collection of orthonormal functions that encodes information about the continued fraction expansion of real numbers. When suitably ordered these functions form a complete system of martingale differences and are a special case of a class of martingale differences considered by R. F. Gundy. By applying known results for martingales we obtain corresponding metric theorems for the continued fraction expansion of almost all real numbers.
Keywords
Cite
@article{arxiv.0906.5428,
title = {Martingale differences and the metric theory of continued fractions},
author = {Alan K. Haynes and Jeffrey D. Vaaler},
journal= {arXiv preprint arXiv:0906.5428},
year = {2009}
}
Comments
Illinois Journal of Mathematics, 2009