Bill Mance

Bill Mance

Adam Mickiewicz University in Poznań

Associate Professor

Published or accepted

  1. Construction of normal numbers with respect to the Q-Cantor series expansion for certain Q, Acta Arith. 148 (2011), no. 2, 135–152
  2. Cantor series constructions contrasting two notions of normality, Monatsh. Math. 164 (2011), no. 1, 1–22 (joint work with C. Altomare)
  3. Typicality of normal numbers with respect to the Cantor series expansion, New York J. Math. 17 (2011), 601–617
  4. Cantor series constructions of sets of normal numbers, Acta Arith. 156 (2012), no. 3, 223–245
  5. Bounded Lüroth expansions: applying Schmidt games where infinite distortion exists, Acta Arith. 158 (2013), no. 1, 33–47 (joint work with J. Tseng)
  6. Number theoretic applications of a class of Cantor series fractal functions. I., Acta Math. Hungar. 144 (2014), no. 2, 449–493
  7. Number theoretic applications of a class of Cantor series fractal functions, II., Int. J. Number Theory 11 (2015), no. 2, 407–435 (joint work with B. Li)
  8. Normal equivalencies for eventually periodic basic sequences, Indag. Math. (N.S.) 26 (2015), no. 3, 476–484 (joint work with D. Airey)
  9. Unexpected distribution phenomenon resulting from Cantor series expansions, Adv. Math. 279 (2015), 372–404 (joint work with D. Airey)
  10. On the Hausdorff dimension of countable intersections of certain sets of normal numbers, J. Théor. Nombres Bordeaux 27 (2015), no. 1, 199–217
  11. Shrinking targets for nonautonomous dynamical systems corresponding to Cantor series expansions, Bull. Aust. Math. Soc. 92 (2015), no. 2, 205–213 (joint work with L. Fishman, D. Simmons, and M. Urbański)
  12. Normality preserving operations for Cantor series expansions and associated fractals, I., Illinois J. Math. 59 (2015), no. 3, 531–543 (joint work with D. Airey)
  13. Normality preserving operations for Cantor series expansions and associated fractals, II. , New York J. Math. 21 (2015), 1311–1326 (joint work with D. Airey and J. Vandehey)
  14. Construction of μ-normal sequences, Monatsh. Math. 179 (2016), no. 2, 259–280 (joint work with M. Madritsch)
  15. The Hausdorff dimension of sets of numbers defined by their Q-Cantor series expansions, J. Fractal Geom. 3 (2016), no. 2, 163–186 (joint work with D. Airey)
  16. Normal number constructions for Cantor series with slowly growing bases, Czechoslovak Math. J. 66(141) (2016), no. 2, 465–480 (joint work with D. Airey and J. Vandehey)
  17. Normality of different orders for Cantor series expansions, Nonlinearity 30 (2017), no. 10, 3719–3742 (joint work with D. Airey)
  18. On the transcendence of certain real numbers, Bull. Aust. Math. Soc. 99 (2019), no. 3, 392–402. (joint work with V. Kumar)
  19. Borel complexity of sets of normal numbers via generic points in subshifts with specification, Trans. Amer. Math Soc. 373 (2020), no. 7, 4561–4584 (joint work with D. Airey, S. Jackson, and D. Kwietniak)
  20. Hotspot lemmas for noncompact spaces, Math. Notes 108 (2020), no. 3-4, 434–439 (joint work with D. Airey)
  21. Some complexity results in the theory of normal numbers, Canad. J. Math. 74 (2022), no. 1, 170–198 (joint work with D. Airey and S. Jackson)
  22. A non-Borel special alpha-limit set in the square, Ergodic Theory Dynam. Systems 42 (2022), no. 8, 2550–2560 (joint work with S. Jackson and S. Roth) VIDEO
  23. Descriptive complexity in Cantor series, J. Symb. Log. 87 (2022), no. 3, 1023–1045 (joint work with D. Airey and S. Jackson)
  24. The descriptive complexity of the set of Poisson generic numbers., J. Math. Log. 25 (2025), no. 2, Paper No. 2450019, 18 pp. (joint work with V. Becher, D. Kwietniak, and S. Jackson)
  25. Borel complexity of sets of points with prescribed Birkhoff averages in Polish dynamical systems with a specification property, Ergodic Theory Dynam. Systems 45 (2025), no. 9, 2695–2723 (joint work with K. Deka, S. Jackson, and D. Kwietniak)

Submitted preprints

  1. On the Borel complexity of continued fraction normal, absolutely abnormal numbers, arXiv (2021) (joint work with S. Jackson and J. Vandehey)
  2. Undecidability in the Ramsey theory of polynomial equations and Hilbert's tenth problem, arXiv (2024) (joint work with S. Farhangi)
  3. Discretized Rotation with fixed initial points, arXiv (2025) (joint work with S. Akiyama)
  4. Borel Complexity of the set of vectors normal for a fixed recurrence sequence, arXiv (2025) (joint work with H. Kaneko)
  5. The Theory of Normality for Dynamically Generated Cantor Series Expansions, arXiv (2025) (joint work with S. Farhangi)