Welcome

Address: Wiedner Hauptstr. 8-10, 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 base-q 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 sum-of-digits function; (3) divisibility of binomial coefficients. I like other beautiful things too, such as piano music.

Research

Publications

Preprints

  1. Lukas Spiegelhofer
    A lower bound for Cusick's conjecture on the digits of n+t
    [ arXiv ]
  2. Lukas Spiegelhofer and Thomas Stoll
    The sum-of-digits function on arithmetic progressions
    [ arXiv | Sage ]
  3. Lukas Spiegelhofer
    The level of distribution of the Thue–Morse sequence
    [ arXiv ]

Journal Papers

  1. Lukas Spiegelhofer
    Approaching Cusick's conjecture on the sum-of-digits function
    Accepted for publication in INTEGERS
    [ arXiv ]
  2. 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 ]
  3. 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 ]
  4. Lukas Spiegelhofer and Michael Wallner
    The Tu–Deng conjecture holds almost surely
    Electron. J. Combin. 26 (2019), no. 1, article P1.28
    [ arXiv ]
  5. Sandro Bettin, Sary Drappeau, and Lukas Spiegelhofer
    Statistical distribution of the Stern sequence
    Comment. Math. Helv. 94 (2019), no. 2, 241–271
    [ arXiv ]
  6. Lukas Spiegelhofer and Michael Wallner
    Divisibility of binomial coefficients by powers of two
    J. Number Theory 192 (2018), 221–239.
    [ arXiv ]
  7. Lukas Spiegelhofer
    Discrepancy results for the Van der Corput sequence
    Unif. Distrib. Theory 13 (2018), no. 2, 57-69
    [ arXiv ]
  8. 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 ]
  9. Lukas Spiegelhofer
    Pseudorandomness of the Ostrowski sum-of-digits function
    J. Théor. Nombres Bordeaux 30 no. 2 (2018), 637-649
    [ arXiv ]
  10. Lukas Spiegelhofer
    A digit reversal property for an analogue of Stern's sequence
    J. Integer Seq. 20 (2017)
    [ arXiv ]
  11. Lukas Spiegelhofer
    A digit reversal property for Stern polynomials
    INTEGERS 17 (2017), Paper No. A53, 7 pp.
    [ arXiv ]
  12. 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 ]
  13. 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 ]
  14. 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 ]
  15. 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 ]
  16. 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 ]
  17. Lukas Spiegelhofer
    Piatetski-Shapiro sequences via Beatty sequences
    Acta Arithmetica 166 (2014), no. 3, 201–229.
    [ arXiv | Abstract | BibTeX | web ]
  18. 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
    Master thesis written under the supervision of Johannes Schoißengeier, Universität Wien, 2011.
    [ PDF ]

Talks

(To be updated)

Miscellaneous

An irrational slide show

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Ilvy
⌊0φ⌋ mod 20= 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
 

(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