Welcome
Address:  Department Mathematics and Information Technology Chair of Mathematics and Statistics Montanuniversität Leoben, FranzJosefStraße 18/HP, 8700 Leoben, Austria 
Room:  44 
Phone:  +43 3842 4023803 
Email:  <firstname>.<lastname>@unileoben.ac.at 
ORCID iD:  000000033552603X 
ResearchGate:  Link 
I am Senior Scientist at the University of Leoben (Austria). My research is centered around, but not restricted to, the baseq representation of an integer. The three main manifestations of this topic in my research concern (0) linear subsequences of substitutive sequences, for example, of the Thue–Morse sequence; (1) understanding addition in terms of digital expansions; (2) divisibility of combinatorially interesting numbers like binomial coefficients. I like other beautiful things too, such as finding mathematics in nature (see below), or piano music.
Research
Publications
Preprints

JeanMarc Deshouillers, Michael Drmota, Clemens Müllner, Andrei Shubin, and Lukas Spiegelhofer
Synchronizing automatic sequences along PiatetskiShapiro sequences
[ arXiv]
Journal Papers

Michael Drmota, Clemens Müllner, and Lukas Spiegelhofer
Primes as sums of Fibonacci numbers (135 pages)
Accepted for publication in Mem. Amer. Math. Soc.
[ arXiv  web ] 
Lukas Spiegelhofer
Collisions of digit sums in bases 2 and 3
Israel J. Math. (2023)
[ arXiv  web ] 
Lukas Spiegelhofer
Gaps in the Thue–Morse word
J. Aust. Math. Soc. 114 (2023), no. 1, 110–144
[ arXiv  web ] 
Myriam Amri, Lukas Spiegelhofer, and Jörg Thuswaldner
Répartition jointe dans les classes de résidus de la somme des chiffres
pour deux représentations d'Ostrowski
Int. J. Number Theory 18 (2022), no. 5, 955–976
[ arXiv  web ] 
Lukas Spiegelhofer and Michael Wallner
The binary digits of n+t
Ann. Sc. Norm. Super. Pisa Cl. Sci. 24 (2023), no. 1, 1–31
[ arXiv  web ] 
Michael Drmota, Christian Mauduit, Joël Rivat, and Lukas Spiegelhofer
Möbius orthogonality for sequences with maximal entropy
J. Anal. Math. (2022), to appear in print
[ arXiv  web ] 
Lukas Spiegelhofer
A lower bound for Cusick's conjecture on the digits of n+t
Math. Proc. Cambridge Philos. Soc 172 (2022), no. 1, 139–161
[ arXiv  pdf ] 
Lukas Spiegelhofer
The level of distribution of the Thue–Morse sequence
Compos. Math. 156 (2020), no. 12, 25602587
[ arXiv  web ] 
Lukas Spiegelhofer and Thomas Stoll
The sumofdigits function on arithmetic progressions
Mosc. J. Comb. Number Theory 9 (2020), no. 1, 4349
[ arXiv  Sage ] 
Lukas Spiegelhofer
Approaching Cusick's conjecture on the sumofdigits function
Integers 19 (2019), Paper No. A59
[ arXiv ] 
JeanMarc Deshouillers, Michael Drmota, Clemens Müllner, and Lukas Spiegelhofer
Randomness and nonrandomness properties of PiatetskiShapiro sequences
modulo m
Mathematika 65 (2019), no. 4, 1051–1073
[ arXiv ] 
Lukas Spiegelhofer and Jeffrey Shallit
Continuants, run lengths, and Barry's modified Pascal triangle
Electron. J. Combin. 26 (2019), no. 1, Paper 1.31
[ arXiv ] 
Lukas Spiegelhofer and Michael Wallner
The Tu–Deng conjecture holds almost surely
Electron. J. Combin. 26 (2019), no. 1, article P1.28
[ arXiv ] 
Sandro Bettin, Sary Drappeau, and Lukas Spiegelhofer
Statistical distribution of the Stern sequence
Comment. Math. Helv. 94 (2019), no. 2, 241–271
[ arXiv ] 
Lukas Spiegelhofer and Michael Wallner
Divisibility of binomial coefficients by powers of two
J. Number Theory 192 (2018), 221–239.
[ arXiv ] 
Lukas Spiegelhofer
Discrepancy results for the Van der Corput sequence
Unif. Distrib. Theory 13 (2018), no. 2, 5769
[ arXiv ] 
Michael Drmota, Clemens Müllner, and Lukas Spiegelhofer
Möbius orthogonality for the Zeckendorf sumofdigits function
Proc. Amer. Math. Soc. 146 (2018), no. 9, 3679–3691.
[ arXiv ] 
Lukas Spiegelhofer
Pseudorandomness of the Ostrowski sumofdigits function
J. Théor. Nombres Bordeaux 30 no. 2 (2018), 637649
[ arXiv ] 
Lukas Spiegelhofer
A digit reversal property for an analogue of Stern's sequence
J. Integer Seq. 20 (2017)
[ arXiv ] 
Lukas Spiegelhofer
A digit reversal property for Stern polynomials
INTEGERS 17 (2017), Paper No. A53, 7 pp.
[ arXiv ] 
Lukas Spiegelhofer and Michael Wallner
An explicit generating function arising in counting binomial coefficients
divisible by powers of primes
Acta Arith. 181 (2017), no. 1, 2755
[ arXiv  Abstract  web ] 
Clemens Müllner and Lukas Spiegelhofer
Normality of the Thue–Morse sequence along PiatetskiShapiro sequences, II
Israel J. Math. 220 (2017), no. 2, 691–738
[ arXiv  Abstract  BibTeX  web ] 
Michael Coons and Lukas Spiegelhofer
The maximal order of hyper(bary) expansions
Electron. J. Combin. 24 (2017), no. 1, Paper 1.15
[ arXiv  Abstract  BibTeX  web ] 
Michael Drmota, Manuel Kauers, and Lukas Spiegelhofer
On a conjecture of Cusick concerning the sum of digits of n and n+t
SIAM J. Discrete Math. 30 (2016), no. 2, 621–649.
[ arXiv  Abstract  BibTeX  web ] 
Lukas Spiegelhofer
Normality of the Thue–Morse sequence along PiatetskiShapiro sequences
Q. J. Math. 66 (2015), no. 4, 1127–1138.
[ arXiv  Abstract  BibTeX  web ] 
Lukas Spiegelhofer
PiatetskiShapiro sequences via Beatty sequences
Acta Arithmetica 166 (2014), no. 3, 201–229.
[ arXiv  Abstract  BibTeX  web ]  Johannes Morgenbesser and Lukas Spiegelhofer
A reverse order property of correlation measures of the sumofdigits function
INTEGERS 12 (2012), Paper No. A47, 5 pp.
[ PDF  Abstract  BibTeX ]
Other publications

Michael Coons and Lukas Spiegelhofer
Number theoretic aspects of regular sequences.
Sequences, groups, and number theory, 37–87, Trends Math., Birkhäuser/Springer, Cham, 2018.
Theses
 Lukas Spiegelhofer
Correlations for numeration systems
PhD thesis written under the joint supervision of Michael Drmota and Joël Rivat, TU Wien and AixMarseille Université, 2014.
[ PDF ]  Lukas Spiegelhofer
Universal properties and categories of modules
Diploma thesis written under the supervision of Johannes Schoißengeier, Universität Wien, 2011.
[ PDF ]
Talks
 Primes as sums of Fibonacci numbers, Teletalk at One World Numeration Seminar October 2022.
 Primes as sums of Fibonacci numbers II, ArithRand 2022, TU Graz, Austria, July 2022
 Subsequences of digitally defined functions, First talk given in the course of obtaining the postdoctoral teaching qualification, TU Wien, Austria, March 2022
 Collisions of digit sums in different bases, Rencontres de théorie analytique et élémentaire des nombres, Paris, March 2022
 The level of distribution of the Thue–Morse sequence, Rencontres de théorie analytique et élémentaire des nombres, Paris, March 2022
 The base2 expansion along arithmetic progressions, Teletalk at the Departmentseminar, Montanuniversität Leoben, Austria, March 2021.
 The digits of n+t, Teletalk at One World Numeration Seminar December 2020.
 The digits of n+t, Teletalk at Séminaire Ernest Marseille, France, October 2020.
 Digital expansions along arithmetic progressions, Montanuniversität Leoben, Austria, March 2020.
 Möbius orthogonality and the sum of digits in different bases, Numeration and Substitution, Vienna, Austria, July 2019.
 The level of distribution of the Zeckendorf sum of digits, Topology of planar and higher dimensional selfreplicating tiles, Strobl, Austria, February 2019.
 The level of distribution of the Thue–Morse sequence, Numeration 2018, Paris, France, May 2018.
 Divisibility of binomial coefficients by powers of primes, ELAZ 2016, Strobl, Austria, September 2016.
 Divisibility of binomial coefficients by powers of primes, Numeration 2016, Prague, Czech Republic, May 2016.
 Divisibility of binomial coefficients by powers of two, Séminaire de Théorie des Nombres de Nancy–Metz, Nancy, France, March 2016.
 Divisibility of binomial coefficients by powers of two, Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, January 2016.
 Divisibility of binomial coefficients by powers of two, Zahlentheoretisches Kolloquium, TU Graz, Austria, January 2016.
 On a problem by Cusick concerning the sum of digits of n and n+t, Automatic sequences, Liège, Belgium, May 2015.
 Normality of the Thue–Morse sequence along PiatetskiShapiro sequences II, Numeration 2015, Nancy, France, May 2015.
 PiatetskiShapiro sequences via Beatty sequences, Pseudorandomness in Number Theory, CIRM (Marseille, France), July 2014.
 The sum of digits of n and n+t, Arbeitsgemeinschaft Diskrete Mathematik, TU Wien, Austria, June 2014.
 Approximating PiatetskiShapiro sequences by Beatty sequences, Séminaire de Théorie des Nombres de Nancy–Metz, Nancy, France, February 2014.
FWF Project
In June 2022 my fouryear FWF project
"Correlations of kregular and morphic sequences" was approved.
Honors and awards
 Edmund und Rosa HlawkaPreis für Mathematik" 2022 by the Austrian Academy of Sciences.
 Joint paper "On a conjecture of Cusick concerning the sum of digits of n and n+t", with Drmota and Kauers, published in SIAM J. Discrete Math., won the best paper award 2017 of the Faculty of Mathematics and Geoinformation, TU Vienna
Short CV
 9/2022–present Senior Scientist at Montanuniversität Leoben
 10/2020–8/2022 University assistant at Montanuniversität Leoben
 02/2017–9/2020 Postdoc at the Vienna University of Technology
 09/2016–01/2017 Postdoc at the JKU Linz, Austria
 02/2016–08/2016 Postdoc at the Université de Lorraine, France
 01/2015–01/2016 Postdoc at the Vienna University of Technology
 2011–2014 PhD studies of mathematics at the Vienna University of Technology and the Aix–Marseille Université under the supervision of Michael Drmota and Joël Rivat.
 2005–2011 Studies of mathematics at the University of Vienna
 2004–2005 Studies of physics at the Vienna University of Technology