Publications

Research interests

Number Theory: Diophantine equations, digit expansions, recurrences, primes, (orthogonal) polynomials, combinatorics on words;

1. (with Y.F. Bilu and R.F. Tichy) Octahedrons with equally many lattice points. Periodica Math. Hung. 40 (2000), 229-238.

2. (with R.F. Tichy) Diophantine equations for continuous classical orthogonal polynomials. Indag. Math. (N.S.) 14 (2003), 263-274.

3. (with R.F. Tichy) The Diophantine equation $\alpha \binom{x}{m}+\beta \binom{y}{n}=\gamma$. Publ. Math. Debrecen 64 (2004), 155-165.

4. Diophantine equations for orthogonal polynomials. Riv. Mat. Univ. Parma 7 (3*) (2004), 311-321.

5. (with R.F. Tichy) Diophantine equations involving general Meixner and Krawtchouk polynomials. Quaest. Math. 28 (2005), 105-115.

6. On a type of nonlinear recurrences related to digits. J. Integer Seq. 8 (2005), Article 05.3.2, 8 pp. (electronic).

7. Multi-parametric extensions of Newman's phenomenon. Integers 5 (3) (2005), A14, 14 pp. (electronic).

8. On a problem of Erdoes and Graham concerning digits. Acta Arith. 125 (2006), 89-100.

9. Octahedrons with equally many lattice points and generalizations. 18th FPSAC (2006), San Diego; poster (refereed).

10. Complete decomposition of Dickson-type recursive polynomials and related Diophantine equations. J. Number Theory 128 (2008), 1157-1181. (Calculation addendum)

11. Complete decomposition of Dickson-type recursive polynomials and related Diophantine equations. 19th FPSAC (2007), Tianjin; poster (refereed).

12. Decomposition of perturbed Chebyshev polynomials. J. Comp. Appl. Math. 214 (2) (2008), 356-370. (Addendum: Data for deg q=5,6,7)

13. (M. Dehmer, M. Drmota, F. Emmert-Streib (Editors); S. Amari, H. Arabnia, M. Beck, A. Solo, Th. Stoll, M. Studeny, N. Tishby, P. Vitanyi (Associate Editors))
    Proceedings of the 2008 Int. Conf. on Information Theory and Statistical Learning. CSREA Press, ISBN: 1-60132-079-5.

14. (with M. Drmota) Newman's phenomenon for generalized Thue-Morse sequences. Discrete Math. 308 (7) (2008), 1191-1208.

15. (with R.F. Tichy) Diophantine equations for Morgan-Voyce and other modified orthogonal polynomials. Math. Slovaca 58 (1) (2008), 11-18.

16. On Hofstadter's married functions. Fibonacci Quart. 46/47 (2008/2009), 62-67.

17. (with M. Drmota and J. Rivat) The sum of digits of primes in Z[i]. Monatsh. Math. 155 (3) (2008), 317-348.

18. Reconstruction problems for graphs, Krawtchouk polynomials and Diophantine equations. Chapter 11, In: Structural Analysis of Complex Networks, Dehmer M. (Editor), Birkhaeuser Publishing (2010), Boston, 293--318.

19. (with J. Zeng) On the total weight of weighted matchings of segment graphs. Electron. J. Combin. R56 (2009), 11pp.

20. (with E. Grant and J. Shallit) Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences. Acta Arith. 140 (2009), 345-368.

21. A fancy way to obtain the binary digits of $759250125\sqrt{2}$. 7pp., Amer. Math. Monthly 117, no.7, August/September 2010, 611-617.

22. (with K.G. Hare and S. Laishram) Stolarsky's conjecture and the sum of digits of polynomial values. Proc. Amer. Math. Soc. 139 (2011), 39-49.

23. (with J. Morgenbesser and J. Shallit) Thue-Morse at multiples of an integer. J. Number Theory 131 (2011), 1498-1512.

24. (with K.G. Hare and S. Laishram) The sum of digits of $n$ and $n^2$. 16pp., IJNT 7 (2011), 1737-1759.

25. The sum of digits of polynomial values in arithmetic progressions. 8pp, Functiones et Approximatio, accepted.

26. (with J. Morgenbesser) On a problem of Chen and Liu concerning the prime power factorization of n!. 11pp, submitted.

Theses:

1. Arithmetic and analytic properties of generalized sequences related to recurrences and digital expansions , Habilitation Thesis (2009), TU Vienna.

2. Finiteness Results for Diophantine Equations Involving Polynomial Families , PhD Thesis (2003), (details)

3. Algorithmic Solution of Diophantine Equations , Diploma Thesis (2001), (details)

Recent selected talks:

• St. Etienne, Séminaire tournant Rhône-Alpes, La valuation p-adique de n! (10/2011)

• Calais, APP 2011, Journée printanière. Sur un problème de Stolarsky : La somme de chiffres de valeurs polynomiales (06/2011).

• Nancy, Journées de théorie analytique des nombres. Somme des chiffres des valeurs polynomiales en base q et en base de Fibonacci (06/2011).

• Vienna, Minikolloquium "Analytische Zahlentheorie und Kombinatorik". Discrete correlation and generalized Rudin-Shapiro sequences (12/2010).

• St. Etienne, Séminaire d'Arithméthique. On Stolarsky's conjectures (10/2010).

• Oberwolfach, Miniworkshop on Combinatorics on Words. On Stolarsky's conjecture: The sum of digits of n and n^h (08/2010).

• Guangzhou, Workshop on Substitutive Tilings and Fractal Geometry. On Newman's phenomenon and related questions (07/2010).

• Paris, Rencontre de théorie analytique et élémentaires des nombres, IHP. On Stolarsky's conjecture: The sum of digits of n and n^h (05/2010).

• Aussois, Workshop, Digital expansions, dynamics and tilings. On Stolarsky's conjecture: The sum of digits of n and n^h (04/2010).

• Marseille, IML, Séminaire "Ernest" 2010 Dynamique, Arithméthique et Combinatoire. Autocorrelation and generalized Rudin-Shapiro sequences (03/2010).

• Marseille, IML, Séminaire "Ernest" 2009 Dynamique, Arithméthique et Combinatoire. Sur un problème de Stolarsky : la somme des chiffres de n et n^h (11/2009).

• Saint Etienne, Université de Saint-Etienne, Jorunées Arithmétiques. Bounds for the discrete correlation of infinite sequences and generalized Rudin-Shapiro sequences (07/2009).

• Ottawa, Carleton University, Conference on Number Theory. Bounds for the discrete correlation of infinite sequences on k symbols and generalized Rudin-Shapiro sequences (06/2009).

• Waterloo, University of Waterloo, Number Theory Seminar. Bounds for the discrete correlation of infinite sequences and generalized Rudin-Shapiro sequences (03/2009).

• Vancouver, University of British Columbia, PIMS/SFU/UBC Number Theory seminar. Coming across Newman's phenomenon, a good many times (09/2008).

• Waterloo, University of Waterloo, Canadian Number Theory Association X Meeting. Newman's phenomenon for generalized Thue-Morse sequences (08/2008).

• Berkeley (CA, USA), UC Berkeley, Berkeley/SFSU Combinatorics Summer Seminar. Octahedrons with equally many lattice points and generalizations (07/2008).

• Montréal, Université du Québec à Montréal, Special Session: "Analytic Number Theory", Second Canada-France Congress. The sum of digits of primes in Z[i] (06/2008).

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Last modified: October 21, 2011