Editorial Duties

Combinatorics and Number Theory (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, together 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, together with A. Huszti, K. Scheicher and P. Surer.
41.) Topology of crystallographic tiles
Geom. Dedicata, 128 (2007) 113 - 144, together 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, together with O. Pfeiffer.
43.) On a family of three term nonlinear integer recurrences
Int. J. Number Theory, 4 (2008) 135 - 146, together 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, together with B. Loridant.
46.) Normality of numbers generated by the values of entire functions
J. Number Theory, 128 (2008) 1127 - 1145, together with M. G. Madritsch and R. F. Tichy.
47.) Generalized radix representations and dynamical systems III
Osaka J. Math., 45 (2008) 347 - 374, together with S. Akiyama, H. Brunotte and A. Pethő.
48.) A new criterion for disk-like crystallographic reptiles
Topology Proc., 31 (2007) 593 - 610, together with B. Loridant and J. Luo.
49.) Weyl Sums in Fq[x] with digital restrictions
Finite Fields Appl., 14 (2008) 877 - 896, together with M. Madritsch.
50.) On the fundamental group of the Sierpinski-gasket
Topology Appl., 156 (2009) 1655 - 1672, together 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, together with T. Beck, H. Brunotte and K. Scheicher.
52.) Generalized radix representations and dynamical systems IV
Indag. Math., 19 (2008) 333 - 348, together with S. Akiyama, H. Brunotte and A. Pethő.
53.) Additive functions for number systems in function fields
Finite Fields Appl., 16 (2010) 204 - 229, together with M. Madritsch.
54.) Interior components of a tile associated to a quadratic canonical number system - Part II
Fractals, 18 (2010) 385 - 397, together with J. Bernat and B. Loridant.
55.) Beta-continued fractions over Laurent series
Publ. Math. Debrecen, 77 (2010) 443 - 463, zusammen mit M. Jellali, M. Mkaouar und 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,
zusammen mit V. Berthé und A. Siegel.
57.) Fractal tiles associated with shift radix systems
Adv. Math., 226 (2011) 139 - 175, together with V. Berthé, A. Siegel, W. Steiner and P. Surer.
58.) Similar dissection of sets
Geom. Dedicata, 150 (2011) 233 - 247, together 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, together with P. Kirschenhofer, A. Pethő, and P. Surer.
60.) On linear combinations of units with bounded coefficients
Mathematika, 57 (2011) 247 - 262, together with V. Ziegler.
61.) Shift radix systems for Gaussian integers and Pethő's Loudspeaker
Publ. Math.Debrecen, 79 (2011) 341 - 356, together 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, together with H. Brunotte and P. Kirschenhofer.
63.) Tilings induced by a class of cubic Rauzy fractals
Theoret. Comput. Sci., 477 (2013) 6 - 31, together with B. Loridant, A. Messaoudi, and P. Surer.
64.) Patterns in rational base number systems
J. Fourier Anal. Appl., 19 (2013) 225 - 250, together 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, together with D. Krenn und V. Ziegler.
66.) On a variant of the Kakeya problem in R
Arch. Math. (Basel), 101 (2013) 395 - 400,
together 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, together with G. Dorfer and R. Winkler.
68.) Problems and conjectures around shift radix systems
Open Problems in Mathematics, 2 (2014) 1 - 5,
together with S. Akiyama, H. Brunotte, A. Pethő, and W. Steiner.
69.) Digit systems over commutative rings
Int. J. Number Theory, 10 (2014) 1459 - 1483, together 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,
together with N. Ouled Azaiz and M. Mkaouar.
71.) Shift radix systems - a survey
RIMS Kôkyûroku Bessatsu, B46 (2014) 1 - 59, together with P. Kirschenhofer.
72.) The Geometry of non-unit Pisot substitutions
Ann. Inst. Fourier (Grenoble), 64 (2014) 1373 - 1417, together with M. Minervino.
73.) Characterization of the numbers which satisfy the height reducing property
Indag. Math. (N.S.), 26 (2015) 24 - 27, together with S. Akiyama and T. Zaïmi.
74.) Comments on the height reducing property II
Indag. Math. (N.S.), 26 (2015) 28 - 39, together with S. Akiyama and T. Zaïmi.
75.) On the Fibonacci Mandelbrot set 
Indag. Math. (N.S.), 26 (2015) 174 - 190, together with V. F. Sirvent.
76.) Salem numbers from a class of star-like trees
J. Number Theory, 153 (2015) 85 - 96, together with H. Brunotte.
77.) Rational self-affine tiles
Trans. Amer. Math. Soc., 367 (2015) 7863 - 7894, together with W. Steiner.
78.) Self-affine manifolds
Adv. Math., 289 (2016) 725 - 783, together with G. R. Conner.
79.) The S-adic Pisot conjecture on two letters
Topology Appl., 205 (2016) 47 - 57, together 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, together 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, together 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, together with P. Kirschenhofer.
84.) Characterization of rational matrices that admit finite digit representations
Linear Algebra Appl., 557 (2018) 350 - 358, together with J. Jankauskas.
85.) Number systems over orders 
Monatsh. Math., 187 (2018) 681 - 704, together with A. Pethő.
86.) Geometry, dynamics, and arithmetic of S-adic shifts
Ann. Inst. Fourier (Grenoble) 69 (2019) 1347 - 1409,  together with V. Berthé and W. Steiner.
87.) Number systems over general orders
Acta Math. Hungar., 159 (2019) 187 - 205, together with J.-H. Evertse, K. Győry, and A. Pethő.
88.)  The finiteness property of shift radix systems with general parameters
Integers, 19 (2019) #A50, together with A. Pethő und M. Weitzer.
89.) Recognizability for sequences of morphisms
Ergodic Theory Dynam. Systems, 39 (2019) 2896 - 2931, together 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, together 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, together with V. Berthe und W. Steiner.
93.) Topology of planar self-affine tiles with collinear digit set
J. Fractal Geom., 8 (2021) 53 - 93, together with S. Akiyama and B. Loridant.
94.) A number system with base -3/2
Amer. Math. Monthly, 129 (2022) 539 - 553, together 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, together with M. G. Madritsch.
97.) Rational matrix digit systems 
Linear and Multilinear Algebra, 71 (2023) 1606 - 1639, together with J. Jankauskas.
98.) Generalizations of Sturmian sequences associated with $N$-continued fraction algorithms
Journal of Number Theory}, 250 (2023) 49 - 83, zusammen mit N. Langeveld and L. Rossi.
99.) Multidimensional continued fractions and symbolic codings of toral translations
J. Eur. Math. Soc. (JEMS), 25 (2023) 4997 - 5057, together with V. Berthé and W. Steiner.
100.) On self-affine tiles that are homeomorphic to a ball
Science China Mathematics, 67 (2024) 45 - 76, together with S.-Q. Zhang.
101.) Weyl sums over integers with digital restrictions
Michigan Math. J., 74 (2024) 189-214, together with I. Shparlinski.
102.) Rational self-affine tiles associated to standard and nonstandard digit systems
Panoramas et Synthèses 62 (2024), 129-160, together with L. Rossi and W. Steiner.

103.) Measure and dimension theory of permeable sets and its applications to fractals
submitted, together with G. Leobacher, T. Rajala und A. Steinicke.
104.) A finiteness condition for complex continued fraction algorithms
submitted, together with C. Kalle und F. M. Sélley.

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page last modified: 2024/11/13 by  Jörg Thuswaldner