50 citations · 89 across the 14 of their papers we have counts for
19 papers
Convergence and combinatorics of the Reverse algorithm
Hiroaki Ito, Niels Langeveld, Jörg Thuswaldner
We study the Reverse algorithm, a multidimensional continued fraction algorithm, which is not unimodular. We show that the Reverse algorithm is ergodic and, by proving that its sec…
Rational self-affine tiles associated to standard and nonstandard digit systems
Lucía Rossi, Wolfgang Steiner, Jörg M. Thuswaldner
We consider digit systems , where is an expanding matrix and the digit set is a suitable subset of . To…
Rational matrix digit systems
Jonas Jankauskas, Jörg M. Thuswaldner
Let be a matrix with rational entries which has no eigenvalue of absolute value and let be the smallest nontrivial $A…
Weyl sums over integers with digital restrictions
Igor E. Shparlinski, Jörg M. Thuswaldner
We estimate Weyl sums over the integers with sum of binary digits either fixed or restricted by some congruence condition. In our proofs we use ideas that go back to a paper by Ban…
A number system with base
Lucía Rossi, Jörg M. Thuswaldner
In the present paper we explore a way to represent numbers with respect to the base using the set of digits . Although this number system shares several prope…
On the second Lyapunov exponent of some multidimensional continued fraction algorithms
Valérie Berthé, Wolfgang Steiner, Jörg Thuswaldner
We study the strong convergence of certain multidimensional continued fraction algorithms. In particular, in the two-dimensional case, we prove that the second Lyapunov exponent of…