On Existance Of Expansion Of A Complex Function
Miodrag Rašković (1979)
Publications de l'Institut Mathématique
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Miodrag Rašković (1979)
Publications de l'Institut Mathématique
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Yan-Hui Qu, Hui Rao, Ya-Min Yang (2005)
Acta Arithmetica
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P. Skibiński (1970)
Annales Polonici Mathematici
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W.H. Echols (1893)
Bulletin of the New York Mathematical Society
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T. V. Narayana, E. Goodman (1969)
Cahiers du Bureau universitaire de recherche opérationnelle Série Recherche
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Nathan Wozny, Luca Q. Zamboni (2001)
Acta Arithmetica
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Peter J. Grabner, Pierre Liardet, Robert F. Tichy (1995)
Acta Arithmetica
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Luís Roçadas (2003)
Acta Arithmetica
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Thomas Stoll (2006)
Acta Arithmetica
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W.H. Echols (1893)
Bulletin of the New York Mathematical Society
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Barat, Guy, Frougny, Christiane, Pethő, Attila (2005)
Integers
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Vilmos Komornik, Anna Chiara Lai, Marco Pedicini (2011)
Journal of the European Mathematical Society
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Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding critical bases for all three-letter alphabets and we establish the fractal nature of these bases...
Diego Marques, Alain Togbé (2011)
Colloquium Mathematicae
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In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.
Zuzana Masáková, Tomáš Vávra (2011)
Kybernetika
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We consider positional numeration system with negative base , as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when is a quadratic Pisot number. We study a class of roots of polynomials , , and show that in this case the set of finite -expansions is closed under addition, although it is not closed under subtraction. A particular example is , the golden ratio. For such , we determine the exact bound on the number of fractional...