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. Thor. 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
J. 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.) 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., to appear, together with W. Steiner.


78.)
Self-affine manifolds
submitted, together with G. R. Conner.
79.) 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: 17. 08. 2015 / Jrg Thuswaldner