Worpitzky's Theorem on continued fractions
نویسندگان
چکیده
منابع مشابه
Duke’s Theorem and Continued Fractions
For uniformly chosen random α ∈ [0, 1], it is known the probability the nth digit of the continued-fraction expansion, [α]n converges to the Gauss-Kuzmin distribution P([α]n = k) ≈ log2(1 + 1/k(k + 2)) as n → ∞. In this paper, we show the continued fraction digits of √ d, which are eventually periodic, also converge to the Gauss-Kuzmin distribution as d → ∞ with bounded class number, h(d). The ...
متن کاملOn multidimensional generalization of the Lagrange theorem on continued fractions ∗
We prove a multidimensional analogue of the classical Lagrange theorem on continued fractions. As a multidimensional generalization of continued fractions we use Klein polyhedra.
متن کاملEpisturmian morphisms and a Galois theorem on continued fractions
We associate with a word w on a finite alphabet A an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of w. Then when |A| = 2 we deduce, using the Sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other. Ma...
متن کاملCMFT-MS 15094 The parabola theorem on continued fractions
Using geometric methods borrowed from the theory of Kleinian groups, we interpret the parabola theorem on continued fractions in terms of sequences of Möbius transformations. This geometric approach allows us to relate the Stern–Stolz series, which features in the parabola theorem, to the dynamics of certain sequences of Möbius transformations acting on three-dimensional hyperbolic space. We al...
متن کاملGeneralized Continued Logarithms and Related Continued Fractions
We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base b. We show that all of our so-called type III continued logarithms converge and all rational numbers have fin...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00318-6