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Spring 2008 Martingale differences and the metric theory of continued fractions
Alan K. Haynes, Jeffrey D. Vaaler
Illinois J. Math. 52(1): 213-242 (Spring 2008). DOI: 10.1215/ijm/1242414129

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 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. "Martingale differences and the metric theory of continued fractions." Illinois J. Math. 52 (1) 213 - 242, Spring 2008. https://doi.org/10.1215/ijm/1242414129

Information

Published: Spring 2008
First available in Project Euclid: 15 May 2009

zbMATH: 1236.11068
MathSciNet: MR2507242
Digital Object Identifier: 10.1215/ijm/1242414129

Subjects:
Primary: 11B57 , 11K50 , 60G46

Rights: Copyright © 2008 University of Illinois at Urbana-Champaign

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Vol.52 • No. 1 • Spring 2008
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