Welcome

Address: Department Mathematics and Information Technology
Chair of Mathematics and Statistics
Montanuniversität Leoben,
Franz-Josef-Straße 18/HP, 8700 Leoben, Austria
Room: 44
Phone: +43 3842 402-3803
Email: <firstname>.<lastname>@unileoben.ac.at
ORCID iD: 0000-0003-3552-603X
ResearchGate: Link

I am Senior Scientist at the University of Leoben (Austria). My research is centered around, but not restricted to, the base-q 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

  1. Jean-Marc Deshouillers, Michael Drmota, Clemens Müllner, Andrei Shubin, and Lukas Spiegelhofer
    Synchronizing automatic sequences along Piatetski-Shapiro sequences
    [ arXiv]

Journal Papers

  1. 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 ]
  2. Lukas Spiegelhofer
    Collisions of digit sums in bases 2 and 3
    Israel J. Math. (2023)
    [ arXiv | web ]
  3. Lukas Spiegelhofer
    Gaps in the Thue–Morse word
    J. Aust. Math. Soc. 114 (2023), no. 1, 110–144
    [ arXiv | web ]
  4. 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 ]
  5. 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 ]
  6. 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 ]
  7. 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 ]
  8. Lukas Spiegelhofer
    The level of distribution of the Thue–Morse sequence
    Compos. Math. 156 (2020), no. 12, 2560-2587
    [ arXiv | web ]
  9. Lukas Spiegelhofer and Thomas Stoll
    The sum-of-digits function on arithmetic progressions
    Mosc. J. Comb. Number Theory 9 (2020), no. 1, 43-49
    [ arXiv | Sage ]
  10. Lukas Spiegelhofer
    Approaching Cusick's conjecture on the sum-of-digits function
    Integers 19 (2019), Paper No. A59
    [ arXiv ]
  11. Jean-Marc Deshouillers, Michael Drmota, Clemens Müllner, and Lukas Spiegelhofer
    Randomness and non-randomness properties of Piatetski-Shapiro sequences
    modulo m
    Mathematika 65 (2019), no. 4, 1051–1073
    [ arXiv ]
  12. 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 ]
  13. Lukas Spiegelhofer and Michael Wallner
    The Tu–Deng conjecture holds almost surely
    Electron. J. Combin. 26 (2019), no. 1, article P1.28
    [ arXiv ]
  14. Sandro Bettin, Sary Drappeau, and Lukas Spiegelhofer
    Statistical distribution of the Stern sequence
    Comment. Math. Helv. 94 (2019), no. 2, 241–271
    [ arXiv ]
  15. Lukas Spiegelhofer and Michael Wallner
    Divisibility of binomial coefficients by powers of two
    J. Number Theory 192 (2018), 221–239.
    [ arXiv ]
  16. Lukas Spiegelhofer
    Discrepancy results for the Van der Corput sequence
    Unif. Distrib. Theory 13 (2018), no. 2, 57-69
    [ arXiv ]
  17. Michael Drmota, Clemens Müllner, and Lukas Spiegelhofer
    Möbius orthogonality for the Zeckendorf sum-of-digits function
    Proc. Amer. Math. Soc. 146 (2018), no. 9, 3679–3691.
    [ arXiv ]
  18. Lukas Spiegelhofer
    Pseudorandomness of the Ostrowski sum-of-digits function
    J. Théor. Nombres Bordeaux 30 no. 2 (2018), 637-649
    [ arXiv ]
  19. Lukas Spiegelhofer
    A digit reversal property for an analogue of Stern's sequence
    J. Integer Seq. 20 (2017)
    [ arXiv ]
  20. Lukas Spiegelhofer
    A digit reversal property for Stern polynomials
    INTEGERS 17 (2017), Paper No. A53, 7 pp.
    [ arXiv ]
  21. 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, 27-55
    [ arXiv | Abstract | web ]
  22. Clemens Müllner and Lukas Spiegelhofer
    Normality of the Thue–Morse sequence along Piatetski-Shapiro sequences, II
    Israel J. Math. 220 (2017), no. 2, 691–738
    [ arXiv | Abstract | BibTeX | web ]
  23. Michael Coons and Lukas Spiegelhofer
    The maximal order of hyper-(b-ary) expansions
    Electron. J. Combin. 24 (2017), no. 1, Paper 1.15
    [ arXiv | Abstract | BibTeX | web ]
  24. 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 ]
  25. Lukas Spiegelhofer
    Normality of the Thue–Morse sequence along Piatetski-Shapiro sequences
    Q. J. Math. 66 (2015), no. 4, 1127–1138.
    [ arXiv | Abstract | BibTeX | web ]
  26. Lukas Spiegelhofer
    Piatetski-Shapiro sequences via Beatty sequences
    Acta Arithmetica 166 (2014), no. 3, 201–229.
    [ arXiv | Abstract | BibTeX | web ]
  27. Johannes Morgenbesser and Lukas Spiegelhofer
    A reverse order property of correlation measures of the sum-of-digits function
    INTEGERS 12 (2012), Paper No. A47, 5 pp.
    [ PDF | Abstract | BibTeX ]

Other publications

  1. 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

  1. Lukas Spiegelhofer
    Correlations for numeration systems
    PhD thesis written under the joint supervision of Michael Drmota and Joël Rivat, TU Wien and Aix-Marseille Université, 2014.
    [ PDF ]
  2. Lukas Spiegelhofer
    Universal properties and categories of modules
    Diploma thesis written under the supervision of Johannes Schoißengeier, Universität Wien, 2011.
    [ PDF ]

Talks

FWF Project

In June 2022 my four-year FWF project "Correlations of k-regular and morphic sequences" was approved.

Honors and awards

  • Edmund und Rosa Hlawka-Preis 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