Editorial Duties

Combinatorics and Number Theory (Editorial Board Member)

Lithuanian Mathematical Journal (Editorial Board Member)

Publications

1.) Analyticcontinuation of a class of Dirichlet series
Abh. Math. Semin. Univ. Hamburg 66 (1996), 281 - 287, with P. J. Grabner.
2.) q-difference equations and their applications to combinatorial problems
Grazer Math. Ber. 328 (1996), 103 - 112.
3.) The sum of digits function in number fields
Bull. London Math. Soc. 30 (1998), 37 - 45.
4.) Asymptotic analysis of a class of functional equations
Aequationes Math. 55 (1998), 91 - 105, with G. Derfel, R. F. Tichy and F. Vogl.
5.) Elementary properties of canonical number systems in quadratic fields
in: Applications of Fibonacci Numbers, Volume 7, G. E. Bergum et al. (eds.), Kluwer Academic Publishers, (1998), 405 - 414.
6.) The fundamental Lemma of Kubilius and the Model of Kubilius in number fields
in: Number Theory, K. Györy et al. (eds.), W. de Gruyter Verlag, (1998), 489 - 499.
7.) Fractal dimension of sets induced by bases of imaginary quadratic fields
Math. Slovaca 48 (1998), 365 - 371.
8.) The sum of digits function in number fields: Distribution in residue classes
J. Number Theory 74 (1999), 111 - 125.
9.) The moments of the sum of digits function in number fields
Can. Math. Bull. 42 (1999), 68 - 77, with B. Gittenberger.
10.) Summatoryfunctions of digital sums occurring in cryptography
Period. Math. Hungar. 38 (1999), 111 - 130.
11.) An Erdös-Kac Theorem for Systems of q-Additive Functions
Indag. Math. (N. S.) 11 (2000), 283 - 291, with R. F. Tichy.
12.) Topological properties of two-dimensional number systems 
J. Théor. Nombres Bordeaux 12 (2000), 69 - 79, with S. Akiyama.
13.) The complex sum of digits function and primes
J. Théor. Nombres Bordeaux 12 (2000), 133 - 146.
14.) On the Sum of Digits Function for Number Systems With Negative Bases
Ramanujan J. 4 (2000), 201 - 220, with P. J. Grabner.
15.) Asymptotic Normality of b-Additive Functions on Polynomial Sequences in the Gaussian Number Field
J. Number Theory 84 (2000), 317 - 341, with B. Gittenberger.
16.) Fractals and Number Systems in Real Quadratic Fields
Acta Math. Hungar. 90 (2001), 253 - 269.
17.) Fractal Properties of Number Systems
Period. Math. Hungar. 42 (2001), 51 - 68, with W. Müller and R. F. Tichy.
18.) Attractors for Invertible Expanding Linear Operators and Number Systems in Z²
Publ. Math. Debrecen 58 (2001), 423 - 440.
19.) Canonical number systems, counting automata and fractals
Math. Proc. Cambridge Philos. Soc. 133 (2002), 163 - 182, with K. Scheicher.
20.) Neighbours of self-affine tiles in lattice tilings
in: Trends in Mathematics: Fractals in Graz 2001, P. Grabner and W. Woess (eds.),
Birkhäuser Verlag (2002), 241 - 262, with K. Scheicher.
21.) Distribution properties of digital expansions arising from linear recurrences
Math. Slovaca 53 (2003), 1--20, with M. Lamberger.
22.) Digit systems in polynomial rings over finite fields
Finite Fields Appl. 9 (2003), 322 - 333, with K. Scheicher.
23.) On the characterization of canonical number systems
Osaka J. Math.41(2004), 327 - 351, with K. Scheicher.
24.) On a generalization of the radix representation - a survey
in: High Primes and Misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams,
Fields Inst. Commun., 41 (2004), 19 - 27, with S. Akiyama, T. Borbély, H. Brunotte and A. Pethő.
25.) On the boundary connectedness of connected tiles
Math. Proc. Cambridge Philos. Soc. 137 (2004), 397 - 410, with J. Luo and S. Akiyama.
26.) Elements of small norm in Shanks' cubic extensions of imaginary quadratic fields
J. Symbolic Comput. 38 (2004), 1471 - 1486, with P. Kirschenhofer.
27.) On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series
Abh. Math. Sem. Univ. Hamburg 74 (2004), 11 - 32, with H. Ishikawa.
28.) A survey on topological properties of tiles related to number systems
Geom. Dedicata 109 (2004), 89 - 105, with S. Akiyama.
29.) On the topological structure of fractal tilings generated by quadratic number systems
Comput. Math. Appl. 49 (2005), 1439 - 1485, with S. Akiyama.
30.) Generalized radix representations and dynamical systems I
Acta Math. Hungar. 108 (2005), 207 - 238, with S. Akiyama, T. Borbély, H. Brunotte and A. Pethő.
31.) Analysis of linear combination algorithms in cryptography
ACM Trans. Algorithms 1 (2005), 123 - 142, with P. J. Grabner, C. Heuberger and H. Prodinger.
32.) Waring's problem with digital restrictions
Israel J. Math. 149 (2005), 317 - 344, with R. F. Tichy.
33.) Generalized radix representations and dynamical systems II
Acta Arith. 121 (2006), 21 - 61, with S. Akiyama, H. Brunotte and A. Pethő.
34.) On Waring's and Tarry's problem with digital restrictions
Elementare und Analytische Zahlentheorie (Tagungsband) Proceedings ELAZ-Conference May 24-28, 2004,
Wolfgang Schwarz and Jörn Steuding (Hg.), Franz Steiner Verlag (2006), 143 - 154, with P. Kirschenhofer and O. Pfeiffer.
35.) Basic properties of shift radix systems
Acta Math. Acad. Paedagog. Nyházi. (N.S.) 22 (2006) 19 - 25, with S. Akiyama, T. Borbély, H. Brunotte and A. Pethő.
36.) Unimodular Pisot substitutions and their associated tiles
J. Théor. Nombres Bordeaux 18 (2006), 487 - 536.
37.) Dynamical directions in numeration
Ann. Inst. Fourier (Grenoble), 56 (2006) 1987 - 2092, with G. Barat, V. Berthé and P. Liardet.
38.) On the fundamental group of self-affine plane tiles
Ann. Inst. Fourier (Grenoble), 56 (2006) 2493 - 2524, with J. Luo.
39.) On a parameterized family of relative Thue equations
Publ. Math. Debrecen 71 (2007), 101 - 139, with C. Lampl and P. Kirschenhofer.
(A list of integers of small norm in simplest cubic fields over $Q(\sqrt{-D})$  is available here)
40.) Three-Dimensional Symmetric Shift Radix Systems
Acta Arith. 129 (2007), 147 - 166, with A. Huszti, K. Scheicher and P. Surer.
41.) Topology of crystallographic tiles
Geom. Dedicata 128 (2007), 113 - 144, with B. Loridant und J. Luo.
42.) Waring's Problem restricted by a system of sum of digits congruences
Quaest. Math. 30 (2007), 513 - 523, with O. Pfeiffer.
43.) On a family of three term nonlinear integer recurrences
Int. J. Number Theory 4 (2008), 135 - 146, with P. Kirschenhofer and A. Pethő.
44.) On disk-like self-affine tiles arising from polyominoes
Methods Appl. Anal. 13 (2006), 351 - 372, with  J. Gmainer.
45.) Interior components of a tile associated to a quadratic canonical number system
Topology Appl. 155 (2008), 667 - 695, with B. Loridant.
46.) Normality of numbers generated by the values of entire functions
J. Number Theory 128 (2008), 1127 - 1145, with M. G. Madritsch and R. F. Tichy.
47.) Generalized radix representations and dynamical systems III
Osaka J. Math. 45 (2008), 347 - 374, with S. Akiyama, H. Brunotte and A. Pethő.
48.) A new criterion for disk-like crystallographic reptiles
Topology Proc. 31 (2007), 593 - 610, with B. Loridant and J. Luo.
49.) Weyl Sums in Fq[x] with digital restrictions
Finite Fields Appl. 14 (2008), 877 - 896, with M. Madritsch.
50.) On the fundamental group of the Sierpinski-gasket
Topology Appl. 156 (2009), 1655 - 1672, with S. Akiyama, G. Dorfer and R. Winkler.
51.) Number systems and tilings over Laurent series
Math. Proc. Cambridge. Philos. Soc. 147 (2009), 9 - 29, with T. Beck, H. Brunotte and K. Scheicher.
52.) Generalized radix representations and dynamical systems IV
Indag. Math. 19 (2008), 333 - 348, with S. Akiyama, H. Brunotte and A. Pethő.
53.) Additive functions for number systems in function fields
Finite Fields Appl. 16 (2010), 204 - 229, with M. Madritsch.
54.) Interior components of a tile associated to a quadratic canonical number system - Part II
Fractals 18 (2010), 385 - 397, with J. Bernat and B. Loridant.
55.) Beta-continued fractions over Laurent series
Publ. Math. Debrecen 77 (2010), 443 - 463, with M. Jellali, M. Mkaouar and K. Scheicher.
56.) Substitutions, Rauzy fractals, and tilings
in: Combinatorics, Automata, and Number Theory (V. Berthé and M. Rigo, eds.),
Encyclopedia of Mathematics and its Applications 135, Cambridge University Press, Cambridge, 2010, pp. 248 - 323,
with V. Berthé und A. Siegel.
57.) Fractal tiles associated with shift radix systems
Adv. Math. 226 (2011), 139 - 175, with V. Berthé, A. Siegel, W. Steiner and P. Surer.
58.) Similar dissection of sets
Geom. Dedicata 150 (2011), 233 - 247, with S. Akiyama, J. Luo, R. Okazaki, and W. Steiner.
59.) Finite and periodic orbits of shift radix systems
J. Théor. Nombres Bordeaux 22 (2010), 421 - 448, with P. Kirschenhofer, A. Pethő, and P. Surer.
60.) On linear combinations of units with bounded coefficients
Mathematika 57 (2011), 247 - 262, with V. Ziegler.
61.) Shift radix systems for Gaussian integers and Pethő's Loudspeaker
Publ. Math.Debrecen 79 (2011), 341 - 356, with H. Brunotte and P. Kirschenhofer.
62.) Contractivity of three dimensional shift radix systems with finiteness property
J. Differ. Equations Appl. 18 (2012), 1077 - 1099, with H. Brunotte and P. Kirschenhofer.
63.) Tilings induced by a class of cubic Rauzy fractals
Theoret. Comput. Sci. 477 (2013), 6 - 31, with B. Loridant, A. Messaoudi, and P. Surer.
64.) Patterns in rational base number systems
J. Fourier Anal. Appl., 19 (2013), 225 - 250, with J. F. Morgenbesser and W. Steiner.
65.) On linear combinations of units with bounded coefficients and double-base digit expansions
Monatsh. Math. 171 (2013), 377 - 394, with D. Krenn und V. Ziegler.
66.) On a variant of the Kakeya problem in R
Arch. Math. (Basel) 101 (2013), 395 - 400, with Y.-L. Deng, C. Hu, S. Long, T.-M. Tang, and L. Xi.
67.) Fundamental groups of one-dimensional spaces
Fund. Math. 223 (2013), 137 - 169, with G. Dorfer and R. Winkler.
68.) Problems and conjectures around shift radix systems
Open Problems in Mathematics 2 (2014), 1 - 5, with S. Akiyama, H. Brunotte, A. Pethő, and W. Steiner.
69.) Digit systems over commutative rings
Int. J. Number Theory 10 (2014), 1459 - 1483, with K. Scheicher, P. Surer and C. van de Woestijne.
70.) Sur les chiffres des nombres premiers translatés,
Funct. Approx. Comment. Math. 51 (2014), 237 - 267, with N. Ouled Azaiz and M. Mkaouar.
71.) Shift radix systems - a survey
RIMS Kôkyûroku Bessatsu B46 (2014), 1 - 59, with P. Kirschenhofer.
72.) The Geometry of non-unit Pisot substitutions
Ann. Inst. Fourier (Grenoble) 64 (2014), 1373 - 1417, with M. Minervino.
73.) Characterization of the numbers which satisfy the height reducing property
Indag. Math. (N.S.) 26 (2015), 24 - 27, with S. Akiyama and T. Zaïmi.
74.) Comments on the height reducing property II
Indag. Math. (N.S.) 26 (2015), 28 - 39, with S. Akiyama and T. Zaïmi.
75.) On the Fibonacci Mandelbrot set
Indag. Math. (N.S.) 26 (2015), 174 - 190, with V. F. Sirvent.
76.) Salem numbers from a class of star-like trees
J. Number Theory 153 (2015), 85 - 96, with H. Brunotte.
77.) Rational self-affine tiles
Trans. Amer. Math. Soc. 367 (2015), 7863 - 7894, with W. Steiner.
78.) Self-affine manifolds
Adv. Math. 289 (2016), 725 - 783, with G. R. Conner.
79.) The S-adic Pisot conjecture on two letters
Topology Appl. 205 (2016), 47 - 57, with V. Berthé, M. Minervino, and W. Steiner.
80.) On cut sets of attractors of iterated function systems
Proc. Amer. Math. Soc. 144 (2016), 4341 - 4356, with B. Loridant, J. Luo, and T. Sellami.
81.) Rational digit systems over finite fields and Christol's Theorem
J. Number Theory 171 (2017), 358 - 390, with M. Loquias, M. Mkaouar, and K. Scheicher.
82.) Discrepancy bounds for β-adic Halton sequences
Number Theory - Diophantine problems, uniform distribution and applications
Festschrift in honour of Robert F. Tichy's 60th birthday
Christian Elsholtz and Peter Grabner (eds.). Springer Verlag, 2017, pp. 423 - 444.
83.) Distribution results on polynomials with bounded roots
Monatsh. Math. 185 (2018), 689 - 715, with P. Kirschenhofer.
84.) Characterization of rational matrices that admit finite digit representations
Linear Algebra Appl. 557 (2018), 350 - 358, with J. Jankauskas.
85.) Number systems over orders
Monatsh. Math. 187 (2018), 681 - 704, with A. Pethő.
86.) Geometry, dynamics, and arithmetic of S-adic shifts
Ann. Inst. Fourier (Grenoble) 69 (2019), 1347 - 1409, with V. Berthé and W. Steiner.
87.) Number systems over general orders
Acta Math. Hungar. 159 (2019), 187 - 205, with J.-H. Evertse, K. Győry, and A. Pethő.
88.)  The finiteness property of shift radix systems with general parameters
Integers 19 (2019), #A50, with A. Pethő und M. Weitzer.
89.) Recognizability for sequences of morphisms
Ergodic Theory Dynam. Systems 39 (2019), 2896 - 2931, with V. Berthé, W. Steiner, and R. Yassawi.
90.) On self-affine tiles whose boundary is a sphere
Trans. Amer. Math. Soc. 373 (2020), 491 - 527, with S. Zhang.
91.) S-adic sequences. A bridge between dynamics, arithmetic, and geometry
In: Akiyama S., Arnoux P. (eds) Substitution and Tiling Dynamics: Introduction to Self-inducing Structures.
Lecture Notes in Mathematics 2273 (2020), 97 - 191. Springer, Cham.
92.) On the second Lyapunov exponent of some multidimensional continued fraction algorithms
Math. Comp. 90 (2021), 883 - 905, with V. Berthe and W. Steiner.
93.) Topology of planar self-affine tiles with collinear digit set
J. Fractal Geom. 8 (2021), 53 - 93, with S. Akiyama and B. Loridant.
94.) A number system with base -3/2
Amer. Math. Monthly 129 (2022), 539 - 553, with L. Rossi.
95.) Sur la repartition jointe de la representation d'Ostrowski dans les classes de residu
Int. J. Number Theory 18 (2022), 955 - 976, with M. Amri and L. Spiegelhofer.
96.) The level of distribution of the sum-of-digits function of linear recurrence number systems
J. Théor. Nombres Bordeaux, 34 (2022), 449 - 482, with M. G. Madritsch.
97.) Rational matrix digit systems
Linear and Multilinear Algebra 71 (2023), 1606 - 1639, with J. Jankauskas.
98.) Generalizations of Sturmian sequences associated with $N$-continued fraction algorithms
J. Number Theory 250 (2023), 49 - 83, with N. Langeveld and L. Rossi.
99.) Multidimensional continued fractions and symbolic codings of toral translations
J. Eur. Math. Soc. (JEMS) 25 (2023), 4997 - 5057, with V. Berthé and W. Steiner.
100.) On self-affine tiles that are homeomorphic to a ball
Sci. China Math. 67 (2024), 45 - 76, with S.-Q. Zhang.
101.) Weyl sums over integers with digital restrictions
Michigan Math. J. 74 (2024), 189 - 214, with I. Shparlinski.
102.) Rational self-affine tiles associated to standard and nonstandard digit systems
Panor. Synthèses 62 (2024), 129 - 160, with L. Rossi and W. Steiner.

103.) Measure and dimension theory of permeable sets and its applications to fractals
Adv. Math. to appear, with G. Leobacher, T. Rajala, and A. Steinicke.

104.) A finiteness condition for complex continued fraction algorithms
submitted, with C. Kalle and F. M. Sélley.

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page last modified: 2025/04/21 by Jörg Thuswaldner