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- W1987759786 abstract "Let x 2 (0; 1] and pn=qn; n 1 be its sequence of Luroth Series convergents. Dene the approximation coecients n = n(x) by n = qnx. In [BBDK] the limiting distribution of the sequence (n)n1 was obtained for a.e. x using the natural extension of the ergodic system underlying the L? uroth Series expansion. Here we show that this can be done without the natural extension. We also will get a bound on the speed of convergence. Using the natural extension we will study the distribution for a.e. x of the sequence (n; n+1)n1 and related sequences like (n + n+1)n1. It turns out that for a.e. x the sequence (n; n+1)n1 is distributed according to a continuous singular distribution function G. Furthermore we will see that two consecutive 's are positively correlated." @default.
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- W1987759786 date "1995-01-01" @default.
- W1987759786 modified "2023-09-24" @default.
- W1987759786 title "On the approximation by Lüroth Series" @default.
- W1987759786 hasPublicationYear "1995" @default.
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