On a $\zeta$ function related to the continued fraction transformation
نویسندگان
چکیده
منابع مشابه
Continued-fraction Expansions for the Riemann Zeta Function and Polylogarithms
It appears that the only known representations for the Riemann zeta function ζ(z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ζ(n) for any integer n ≥ 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n ≥ 1, by using the classical Stieltjes technique. Our...
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We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 1976
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.1825