Martingale differences and the metric theory of continued fractions

Haynes, Alan K.; Vaaler, Jeffrey D.

Illinois J. Math., Tome 52 (2008) no. 1, p. 213-242 / Harvested from Project Euclid

Résumé

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.

Publié le : 2008-05-15
Classification: 11B57, 11K50, 60G46

@article{1242414129,
     author = {Haynes, Alan K. and Vaaler, Jeffrey D.},
     title = {Martingale differences and the metric theory of continued fractions},
     journal = {Illinois J. Math.},
     volume = {52},
     number = {1},
     year = {2008},
     pages = { 213-242},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1242414129}
}

Haynes, Alan K.; Vaaler, Jeffrey D. Martingale differences and the metric theory of continued fractions. Illinois J. Math., Tome 52 (2008) no. 1, pp.  213-242. http://gdmltest.u-ga.fr/item/1242414129/