A set of infinite measure whose ratio set does not contain a given sequence.
J.A. HAIGHT (1974/1975)
Seminaire de Théorie des Nombres de Bordeaux
Foo, Timothy (2007)
Integers
Riho Terras (1976)
Acta Arithmetica
Władysław Narkiewicz, Tibor Šalát (1984)
Czechoslovak Mathematical Journal
Joël Rivat, András Sárközy (2010)
Acta Arithmetica
Martijn de Vrie, Vilmos Komornik (2011)
Fundamenta Mathematicae
Let J ⊂ ℝ² be the set of couples (x,q) with q > 1 such that x has at least one representation of the form with integer coefficients satisfying , i ≥ 1. In this case we say that is an expansion of x in base q. Let U be the set of couples (x,q) ∈ J such that x has exactly one expansion in base q. In this paper we deduce some topological and combinatorial properties of the set U. We characterize the closure of U, and we determine its Hausdorff dimension. For (x,q) ∈ J, we also prove new properties...
József Beck (1989)
Compositio Mathematica
Sebe, Gabriela Ileana (2005)
International Journal of Mathematics and Mathematical Sciences
F. Schweiger (1972)
Monatshefte für Mathematik
Tibor Šalát (1959)
Czechoslovak Mathematical Journal
G. Jogesh Babu (1975)
Acta Arithmetica
Daniel Berend (1987)
Acta Arithmetica
Stephan Baier (2005)
Acta Arithmetica
J. De Koninck, I. Kátai, A. Mercier (1991)
Acta Arithmetica
I. Kátai, P. Liardet (2001)
Acta Arithmetica
Eduard Wirsing (1980)
Acta Arithmetica
Yves Meyer (1971/1972)
Séminaire Delange-Pisot-Poitou. Théorie des nombres
Yusuf Hartono, Cor Kraaikamp, Fritz Schweiger (2002)
Journal de théorie des nombres de Bordeaux
In this paper the Engel continued fraction (ECF) expansion of any is introduced. Basic and ergodic properties of this expansion are studied. Also the relation between the ECF and F. Ryde’s monotonen, nicht-abnehmenden Kettenbruch (MNK) is studied.
Hajime Kaneko (2012)
Acta Arithmetica
P. Blanksby, H. Montgomery (1971)
Acta Arithmetica