Welcome
Address:  Wiedner Hauptstr. 810, 1040 Wien, Austria 
Room:  DA05 F22, Freihaus, green tower, 5th floor 
Email:  firstname.lastname@tuwien.ac.at 
I am currently a postdoc at the TU Vienna (Austria) and employed in the FWF special research project Quasi Monte Carlo Methods: Theory and Applications. My research is centered around, but not restricted to, the baseq representation of an integer. The two main manifestations of this topic in my research concern (1) linear subsequences of the Thue–Morse sequence; (2) correlations of the sumofdigits function; (3) divisibility of binomial coefficients. I like other beautiful things too, such as piano music.
Research
Publications
Preprints
Journal Papers

Lukas Spiegelhofer and Thomas Stoll
The sumofdigits function on arithmetic progressions
Accepted for publication in Mosc. J. Comb. Number Theory
[ arXiv  Sage ] 
Lukas Spiegelhofer
Approaching Cusick's conjecture on the sumofdigits function
Accepted for publication in INTEGERS
[ 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
Master thesis written under the supervision of Johannes Schoißengeier, Universität Wien, 2011.
[ PDF ]
Talks
(To be updated)
 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.
Miscellaneous
An irrational slide show
(Activate JavaScript for best results)
(Here φ is the golden ratio. Note that with 21 images there would be long runs of repeats, since we have the continued fraction φ/21=[0;12,1,45,1,45,1,45,…], while φ/20=[0; 12, 2, 1, 3, 2, 1, 1, 10, 1, 1,…]. Also note what happens to the multiple if the numbers are clicked in a row! )
Short CV
 02/2017–present 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