STOLL Thomas

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).

Articles/Posters/Book chapters:

• (with Y.F. Bilu and R.F. Tichy) Octahedrons with equally many lattice points, Periodica Math. Hung. 40 (2000), 229-238.
• (with R.F. Tichy) Diophantine equations for continuous classical orthogonal polynomials, Indag. Math. (N.S.) 14 (2003), 263-274.
• (with R.F. Tichy) The Diophantine equation $\alpha \binom{x}{m}+\beta \binom{y}{n}=\gamma$, Publ. Math. Debrecen 64 (2004), 155-165.
• Diophantine equations for orthogonal polynomials, Riv. Mat. Univ. Parma 7 (3*) (2004), 311-321.
• (with R.F. Tichy) Diophantine equations involving general Meixner and Krawtchouk polynomials, Quaest. Math. 28 (2005), 105-115.
• On a type of nonlinear recurrences related to digits, J. Integer Seq. 8 (2005), Article 05.3.2, 8 pp. (electronic).
• Multi-parametric extensions of Newman’s phenomenon, Integers 5 (3) (2005), A14, 14 pp. (electronic).
• On a problem of Erdoes and Graham concerning digits, Acta Arith. 125 (2006), 89-100.
• Octahedrons with equally many lattice points and generalizations. 18th FPSAC (2006), San Diego; poster (refereed).
• Complete decomposition of Dickson-type recursive polynomials and related Diophantine equations, J. Number Theory 128 (2008), 1157-1181.
• Complete decomposition of Dickson-type recursive polynomials and related Diophantine equations, 19th FPSAC (2007), Tianjin; poster (refereed).
• Decomposition of perturbed Chebyshev polynomials, J. Comp. Appl. Math. 214 (2) (2008), 356-370.
• (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.
• (with M. Drmota) Newman’s phenomenon for generalized Thue-Morse sequences, Discrete Math. 308 (7) (2008), 1191-1208.
• (with R.F. Tichy) Diophantine equations for Morgan-Voyce and other modified orthogonal polynomials, Math. Slovaca 58 (1) (2008), 11-18.
• On Hofstadter’s married functions, Fibonacci Quart. 46/47 (2008/2009), 62-67.
• (with M. Drmota and J. Rivat) The sum of digits of primes in Z[i], Monatsh. Math. 155 (3) (2008), 317-348.
• 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.
• (with J. Zeng) On the total weight of weighted matchings of segment graphs, Electron. J. Combin. R56 (2009), 11pp.
• (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.
• A fancy way to obtain the binary digits of $759250125\sqrt{2}$. Amer. Math. Monthly 117, no.7, August/September 2010, 611-617.
• (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.
• (with J. Morgenbesser and J. Shallit) Thue-Morse at multiples of an integer, J. Number Theory 131 (2011), 1498-1512.
• (with K.G. Hare and S. Laishram) The sum of digits of $n$ and $n^2$, Int. Journal of Number Theory, Vol. 07, No. 07, pp. 1737-1752 (2011).
• The sum of digits of polynomial values in arithmetic progressions, Functiones et Approximatio 47 (2) (2012), 233-239.
• (with J. Morgenbesser) On a problem of Chen and Liu concerning the prime power factorization of n!, Proc. Amer. Math. Soc. (2013), 2289-2297.
• (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.
• Combinatorial constructions for the Zeckendorf sum of digits of polynomial values, Ramanujan J. 32 (2013), 227-243.
• (with M. Madritsch) On simultaneous digital expansions of polynomial values, Acta Math. Hungarica 143 (1) (2014), 192-200.
• (with M. Madritsch) On a second conjecture of Stolarsky: the sum of digits of polynomial values, Archiv der Mathematik (Basel) 102 (2014), 49-57.
• Thue-Morse along two polynomial subsequences, Lecture Notes in Computer Science, Springer, LNCS 9304 (2015), Chapter 5, 47-58.
• On digital blocks of polynomial values and extractions in the Rudin-Shapiro sequence, RAIRO – Theoretical Informatics and Applications 50 (1) (2016), 93-99.
• (with H. Kaneko), On subwords in the base-q expansion of polynomial and exponential functions, Integers, vol. 18A (2018).
• (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.
• (with H. Kaneko), Hensel’s lemma for general continuous functions, Indagationes Math. 30 (4) (2019), 610-622.
• (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.
• (with L. Spiegelhofer), The sum-of-digits function on arithmetic progressions, Moscow Journal of Combinatorics and Number Theory, Vol. 9 (2020), No. 1, 43–49.
• (with I.Marcovici and P.-A. Tahay) Discrete correlations of order 2 of generalised Golay-Shapiro sequences: a combinatorial approach, Integers, 21pp, to appear (2021).

Responsable S2 Maths-Info (Université de Lorraine, Nancy)

2012-, Professeur des universités (tenured position), IECL, Université de Lorraine, Nancy

2009-2012, Maître de conférences (tenured position), IML, Université de la Méditerranée / Université d’Aix-Marseille, Marseille

2009, Habilitation in “Discrete Mathematics”, TU Vienna

2008-2009, Visiting Researcher by APART grant (Austrian Programme for Advanced Research and Technology) of the Austrian Academy of Sciences at University of Waterloo, Canada

2006-2008, Collaborator (Postdoc) in the NFN S9600 (National Research Network: “Analytic Combinatorics and Probabilistic Number Theory”, TU Vienna) of the Austrian Science Foundation

2005-2006, Assistant Professor at University of Vienna

2002-2005, Collaborator (PhD student, Postdoc) in the FSP-Projects S8307-MAT (“Numbertheoretic Algorithms and Applications”, TU Graz) and S8302-MAT (“Statistical Properties of Number Systems”, TU Vienna) of the Austrian Science Foundation

2004, “Promotio sub auspiciis Praesidentis”, “Wuerdigungpreis” of the Austrian Federal Ministry for Education, Science and Culture

2001-2003, PhD-Studies in Mathematics at TU Graz
Thesis: Finiteness Results for Diophantine Equations Involving Polynomial Families (Advisor: R.F. Tichy)

1997-2001, Study of Technical Mathematics at TU Graz, branch: Technomathematics
Diploma Thesis: Algorithmic Solution of Diophantine Equations (Advisor: R.F. Tichy)

Some selected talks:

• CIRM, Marseille, Prime Numbers, Determinism and Pseudorandomness On a problem of Erdoes concerning the digits of 2^n in base 3 and Hensel’s lemma (11/2019)
• Jinan, Mathematics and Music – two magical horns, Lecture given for a secondary school class, Jinan, China (10/2019)
• Jinan/Tianjin/Hongkong/Macao/Xi’an, China, Seminars and Colloquia (09/2019-10/2019)
• Kiel, WORDS 2015 (09/2015)
• Nancy, Journées Montoises d’Informatique Théorique. Correlations and subsequences in Rudin-Shapiro words : a survey (09/2014)
• Graz, Zahlentheoretisches Kolloquium. On the p-adic valuation of factorials and their subsequences (03/2012)
• Banff, Workshop: Outstanding Challenges in Combinatorics on Words (BIRS). Thue-Morse at polynomial subsequences (02/2012)
• 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).

Bassoon/Basson – Study of the bassoon under the supervision of Prof. Faludy (KUG Graz, Final Diploma Concert with highest distinction, 01/2008), Graduation to MA (Master of Arts).

Chinese/Chinois – Language Courses taken at Zuerich and Beijing, HSK Level 5 (new system).

Chess/Échecs – Elo international 2092 (02/2021), Italian “Maestro” title, 3 times Vice-Champion in Italian Junior Championships.

Piano – Awards in the musical competitions “Jugend musiziert” and “Prima la musica”.