More on inhomogeneous diophantine approximation
For an irrational real number and real number we consider the inhomogeneous approximation constantvia the semi-regular negative continued fraction expansion of
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Christopher G. Pinner (2001)
Journal de théorie des nombres de Bordeaux
For an irrational real number and real number we consider the inhomogeneous approximation constantvia the semi-regular negative continued fraction expansion of
Yann Bugeaud, Dalia Krieger, Jeffrey Shallit (2011)
Acta Arithmetica
Lascoux, Alain (2000)
Séminaire Lotharingien de Combinatoire [electronic only]
Zongduo Dai, Kunpeng Wang, Dingfeng Ye (2006)
Acta Arithmetica
H.R.P. Ferguson, R.W. Forcade (1982)
Journal für die reine und angewandte Mathematik
Oleg Karpenkov (2013)
Journal de Théorie des Nombres de Bordeaux
In this paper we describe the set of conjugacy classes in the group . We expand geometric Gauss Reduction Theory that solves the problem for to the multidimensional case, where -reduced Hessenberg matrices play the role of reduced matrices. Further we find complete invariants of conjugacy classes in in terms of multidimensional Klein-Voronoi continued fractions.
Henri COHEN (1972/1973)
Seminaire de Théorie des Nombres de Bordeaux
Henri Cohen (1974)
Acta Arithmetica
J. Loxton, Alfred van der Poorten (1983)
Acta Arithmetica
Florian Luca, Volker Ziegler (2013)
Acta Arithmetica
Given a binary recurrence , we consider the Diophantine equation with nonnegative integer unknowns , where for 1 ≤ i < j ≤ L, , and K is a fixed parameter. We show that the above equation has only finitely many solutions and the largest one can be explicitly bounded. We demonstrate the strength of our method by completely solving a particular Diophantine equation of the above form.
Victor Beresnevich, Alan Haynes, Sanju Velani (2013)
Acta Arithmetica
We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete 'multiplicative' zero-one law is established akin to the 'simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile 'cross fibering principle'. In a nutshell it enables us to 'lift' zero-one laws to higher...
Carlos Alexis Ruiz Gómez, Florian Luca (2015)
Acta Arithmetica
We consider the Tribonacci sequence given by T₀ = 0, T₁ = T₂ = 1 and for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.
Evgeniy Zorin (2012)
Journal de Théorie des Nombres de Bordeaux
We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan’s classical differential relations. This result can be useful in the study of arithmetic properties of values of Riemann zeta function at odd positive integers (Nesterenko, 2011).
Michael Nakamaye (1995)
Bulletin de la Société Mathématique de France
D.W. Masser, W.D. Brownawell (1980)
Journal für die reine und angewandte Mathematik
Vincent Bosser (2008)
Acta Arithmetica
D. V. Choodnovsky, G. V. Choodnovsky (1977/1978)
Séminaire sur les équations non linéaires (Choodnovsky)
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