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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)

It is well known that each positive integer n can be expressed uniquely as a sum n = d0 + d1b + . . . + dhb h with an integral base number b ≥ 2, dh 6= 0 and di ∈ {0, . . . , b − 1}. This concept can be generalized in several directions. On the one hand the base sequence 1, b, b, . . . can be replaced by a sequence 1 = u0 < u1 < u2 < . . . to obtain… (More)

where the γi are again continuous fluctuations of period 1. All these results can be extended to so-called canonical number systems. We recall the definition of these number systems: Definition 1.1. Let K be a number field and ZK its ring of integers. A pair (b,N ) with b ∈ ZK and N = {0, 1, . . . , |N(b)| − 1} is called canonical number system if any γ ∈… (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)

- Wolfgang Müller, Jörg M. Thuswaldner, Robert F. Tichy
- Periodica Mathematica Hungarica
- 2001

- Manfred G. Madritsch, Jörg M. Thuswaldner
- Finite Fields and Their Applications
- 2008

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)

- JÖRG THUSWALDNER
- 2010

Starting with a paper of Jacobson form the 1960s, many authors became interested in characterizing all algebraic number fields in which each integer is the sum of pairwise distinct units. Although there exist many partial results for number fields of low degree, a full characterization of these number fields is still not available. Narkiewicz and Jarden… (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)