Martingale differences and the metric theory of continued fractions

AK Haynes, J Vaaler

Research output: Contribution to journalArticle (Academic Journal)peer-review

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.
Translated title of the contributionMartingale differences and the metric theory of continued fractions
Original languageEnglish
Pages (from-to)213 - 242
Number of pages30
JournalIllinois Journal of Mathematics
Volume52, number 1
Publication statusPublished - Mar 2008

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