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arXiv · 0906.5428

Martingale differences and the metric theory of continued fractions

Alan K. Haynes·Jeffrey D. Vaaler
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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.

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Alan K. Haynes, Jeffrey D. Vaaler. 2009-06-30. Martingale differences and the metric theory of continued fractions. https://arxiv.org/abs/0906.5428

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