Johann Verwee

PhD in Mathematics

Analytic and Probabilistic Number Theory

Numeration Systems, Short Intervals, and Distribution Problems

CV (PDF)

Research

Thesis and Master's thesis

Contact

Email: mverwee (at) gmail [dot] com

Research interests

Quantitative limit theorems in number theory (Erdős–Wintner, Berry–Esseen)
Short intervals: mean values and fluctuations
Numeration systems / structured digit expansions
Probabilistic models and finite-memory (automaton/transducer) methods
Numerical experiments and computational number theory

I work in analytic and probabilistic number theory, with a focus on quantitative limit laws (Erdős–Wintner, Berry–Esseen) for additive functions and structured digit models in numeration systems.

My research combines probabilistic and analytic methods with finite-memory models (automata/transducers) when relevant. I also run numerical experiments to test heuristics and to support intuition.

I am currently applying for postdoctoral positions and welcome discussions and collaborations.

Publications

4. Short intervals for the Romanoff-type sumset (with Y. Ding), Journal of Number Theory, 289 (2026), 114-131.

DOI: 10.1016/j.jnt.2026.04.002.

3. Effective Erdős-Wintner theorem for Cantor numeration systems via a trailing-window method, International Journal of Number Theory, 22,

no. 6 (March 2026), 1175-1194. DOI: 10.1142/S1793042126500636.

2. Effective Erdős-Wintner theorems for digital expansions (with M. Drmota), Journal of Number Theory, 229 (December 2021), 218-260.

DOI: 10.1016/j.jnt.2021.04.006.

1. Effective Erdős-Wintner theorems (with G. Tenenbaum), Proc. Steklov Inst. Math., 314 (September 2021), 264-278.

DOI: 10.1134/S008154382104012X.

Preprints

5. Linear truncation on conditioned prime-factor fibres (March 2026).

4. A semigroup approach to iterated binomial transforms (January 2026).

3. Diagonal symmetrisation of tridiagonal Toeplitz matrices (January 2026).

2. A spectral product formula for repunits via a tridiagonal Toeplitz similarity (December 2025).

1. Improvement of effective Erdős-Wintner theorem for Zeckendorf expansions (September 2025).

Under review

1. Erdős-Wintner theorem for linear recurrent bases, under review.

In preparation

2. A Dirichlet-type theorem for terminal blocks of primes in Pisot numeration systems (with S. Chang).

1. A finite-state Erdős-Wintner theorem.

Talks

Numeration 2026, Vandœuvre-lès-Nancy (France), June 5, 2026.
Number Theory Seminar, Charles University, Prague, March 11, 2026 (online).
Nancy-Metz Number Theory Seminar, IECL, December 10, 2021 (online).
Ernest Seminar, Institut de Mathématiques de Marseille, May 11, 2021 (online).
Nancy-Metz PhD Students' Day, October 2, 2020.
Nancy-Metz PhD Students' Day, May 17, 2018.

Curriculum Vitae

My CV is here.

Thesis and Master's thesis

PhD thesis (in French): Théorèmes d’Erdős-Wintner effectifs, joint supervision between Université de Lorraine and Technische Universität Wien, under the supervision of Professors G. Tenenbaum and M. Drmota, defended on November 20, 2020.

Master's thesis (in French): La fonction lambda de Liouville dans les petits intervalles, supervised by G. Tenenbaum, Université de Lorraine, 2016.