Jörg M. Thuswaldner

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Abstract. For r = (r1, . . . , rd) ∈ R d the mapping τr : Z → Z given by τr(a1, . . . , ad) = (a2, . . . , ad,−⌊r1a1 + · · ·+ rdad⌋) where ⌊·⌋ denotes the floor function, is called a shift radix system if for each a ∈ Z there exists an integer k > 0 with τ r (a) = 0. As shown in Part I of this series of papers, shift radix systems are intimately related to(More)
0. Notations Throughout the paper we use the following notations: We write e(z) = e; C, R, Q, Z, N and N0, denote the set of complex numbers, real numbers, rational numbers, integers, positive integers, and positive integers including zero, respectively. Q(i) denotes the field of Gaussian numbers, and Z[i] the ring of Gaussian integers. We write tr(z) and(More)
Let Fq be a finite field and consider the polynomial ring Fq [X]. Let Q ∈ Fq [X]. A function f : Fq [X] → G, where G is a group, is called strongly Q-additive, if f(AQ + B) = f(A) + f(B) holds for all polynomials A,B ∈ Fq [X] with degB < degQ. We estimate Weyl Sums in Fq [X] restricted by Q-additive functions. In particular, for a certain character E we(More)
The aim of the present paper is to generalize earlier work by Thuswaldner and Tichy on Waring’s Problem with digital restrictions to systems of digital restrictions. Let sq(n) be the q-adic sum of digits function and let d, s, al, ml, ql ∈ N. Then for s > d ( log d+ log log d+O(1) ) there exists N0 ∈ N such that each integer N ≥ N0 has a representation of(More)
Let σ be a unimodular Pisot substitution over a d letter alphabet and let X1, . . . , Xd be the associated Rauzy fractals. In the present paper we want to investigate the boundaries ∂Xi (1 ≤ i ≤ d) of these fractals. To this matter we define a certain graph, the so-called contact graph C of σ. If σ satisfies Manuscrit reçu le 17 novembre 2004. The author(More)
In this paper we study properties of the fundamental domain Fβ of number systems, which are defined in rings of integers of number fields. First we construct addition automata for these number systems. Since Fβ defines a tiling of the n-dimensional vector space, we ask, which tiles of this tiling “touch” Fβ . It turns out, that the set of these tiles can be(More)