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Article overview
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Martingale differences and the metric theory of continued fractions | Alan K. Haynes
; Jeffrey D. Vaaler
; | Date: |
30 Jun 2009 | 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. | Source: | arXiv, 0906.5428 | Services: | Forum | Review | PDF | Favorites |
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