ao.Univ.Prof.Dipl.-Ing.Dr.techn.
Jrg M. Thuswaldner

Sprechstunden: Di, Mi 10-11

email: Joerg.Thuswaldner@unileoben.ac.at
Tel.: ++43/ +3842 - 402 - 3805


Publications
(Copyright of all papers either by the author or by the publisher)

1.) Analytic continuation 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. Gyry 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.)
Summatory functions of digital sums occurring in cryptography
Period. Math. Hungar., 38 (1999), 111 - 130.
11.)
An Erds-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. Thor. Nombres Bordeaux, 12 (2000) 69 - 79, with S. Akiyama.
13.)
The complex sum of digits function and primes
J. Thor. 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. Mller and R. F. Tichy.
18.)
Attractors for Invertible Expanding Linear Operators and Number Systems in Z
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.),
Birkhuser 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. Peth.
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. Borbly, H. Brunotte and A. Peth.
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. Peth.
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 Jrn 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. Nyhzi. (N.S.), 22 (2006) 19 - 25,
with S. Akiyama, T. Borbly, H. Brunotte and A. Peth.
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. Berth 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. Peth.
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. Peth.
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. Peth.
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. Berth and M. Rigo, eds.),
Encyclopedia of Mathematics and its Applications 135, Cambridge University Press, Cambridge, 2010, pp. 248 - 323,
zusammen mit V. Berth und A. Siegel.
57.
Fractal tiles associated with shift radix systems
Adv. Math., 226 (2011) 139 - 175, together with V. Berth, 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
Journal de Thor. Nombres Bordeaux, 22 (2010) 421 - 448, together with P. Kirschenhofer, A. Peth, 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 Peth'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. Peth, 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 translats,
Funct. Approx. Comment. Math., 51 (2014) 237 - 267,
together with N. Ouled Azaiz and M. Mkaouar.
71.
Shift radix systems - a survey
RIMS Kkyroku 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. Zami.
74. Comments on the height reducing property II
Indag. Math. (N.S.), 26 (2015) 28 - 39, together with S. Akiyama and T. Zami.
75. On the Fibonacci Mandelbrot set
Indag. Math. (N.S.), 26 (2015) 174 - 190, together with V. F. Sirvent.

76. Rational self-affine tiles
Trans. Amer. Math. Soc., to appear, together with W. Steiner.

77.
Self-affine manifolds
submitted, together with G. R. Conner.
78. Geometry, dynamics, and arithmetic of S-adic shifts
submitted, together with V. Berth and W. Steiner.


If you are interested in one of the papers which are not downloadable, please don't hesitate to contact me via e-mail.

 

page last modified: 10. 12. 2014 / Jrg Thuswaldner