Publications


Research interests

Analytic and combinatorial number theory – Combinatorics on words

Keywords:Diophantine equations, digital expansions, recurrences, primes, (orthogonal) polynomials




  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 $759250125\sqrt{2}$. 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 $n^2$. International Journal of Number Theory, Vol. 07, No. 07, pp. 1737-1752 (2011).

  25. The sum of digits of polynomial values in arithmetic progressions. Functiones et Approximatio 47 (2) (2012), 233-239.

  26. (with J. Morgenbesser) On a problem of Chen and Liu concerning the prime power factorization of n!. Proc. Amer. Math. Soc. (2013), 2289-2297.

  27. (with I. Boreico and D. El-Baz) On a conjecture of Dekking : The sum of digits of even numbers. J. Théorie Nombres Bordeaux (2014), 17-24.

  28. Combinatorial constructions for the Zeckendorf sum of digits of polynomial values. Ramanujan J. 32 (2013), 227-243.

  29. (with M. Madritsch) On simultaneous digital expansions of polynomial values, Acta Math. Hungarica 143 (1) (2014), 192-200.

  30. (with M. Madritsch) On a second conjecture of Stolarsky: the sum of digits of polynomial values, Archiv der Mathematik (Basel) 102 (2014), 49-57.

  31. Thue-Morse along two polynomial subsequences, Lecture Notes in Computer Science, Springer, LNCS 9304 (2015), Chapter 5, 47-58.

  32. On digital blocks of polynomial values and extractions in the Rudin-Shapiro sequence, RAIRO - Theoretical Informatics and Applications 50 (1) (2016), 93-99.

  33. (with H. Kaneko), On subwords in the base-q expansion of polynomial and exponential functions, Integers, vol. 18A (2018).

  34. (with I. Marcovici and P.A. Tahay), Construction of some nonautomatic sequences by cellular automata, Lecture Notes in Computer Science, Springer, LNCS 10875 (2018), 113-126.

  35. (with H. Kaneko), Hensel's lemma for general continuous functions, Indagationes Math. 30(4) (2019), 610-622.

  36. (with R. de la Bretèche and G. Tenenbaum), Somme des chiffres et changement de base, Annales de l'Institut Fourier, Volume 69 (2019) no. 6, p. 2507-2518.

  37. (with L. Spiegelhofer), The sum-of-digits function on arithmetic progressions, Moscow Journal of Combinatorics and Number Theory, to appear (2019).



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)



Some selected talks:


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Last modified: December 10, 2019