Johann Verwee

PhD in Mathematics

Analytic and Probabilistic Number Theory

Limit Theorems, Numeration Systems, and Digital Expansions

CV (PDF)

Research

PhD and Master's thesis

Contact

Email: mverwee (at) gmail [dot] com

Research interests

Limit laws for arithmetic functions
Effective Erdős–Wintner-type theorems
Numeration systems and digital expansions
Arithmetic properties of digital representations

I work mainly in analytic and probabilistic number theory. I am particularly interested in limit laws for arithmetic functions and their effective versions, especially around the Erdős–Wintner theorem.

A substantial part of my research concerns numeration systems and digital expansions, as well as arithmetic properties arising in these systems.

My research combines analytic and probabilistic methods, often complemented by numerical experiments to test heuristics and 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 (December 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.

Research notes not intended for publication

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).

Manuscripts in preparation

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

1. An Erdős–Wintner theorem for second-order linear recurrent bases.

Talks and presentations

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.

PhD and master's theses

PhD thesis (in French): Théorèmes d’Erdős-Wintner effectifs, completed under a joint PhD agreement between Université de Lorraine and Technische Universität Wien, supervised by 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.

A few words about me

Erdős number: 2.
Languages: French, English and German; currently learning Mandarin Chinese.
Chess: club player, FIDE rating 1888 (peak: 1906).
Travel: I lived in Austria for two years and travelled to Germany, Ireland, Poland and the United Kingdom (London and Northern Ireland).
Manga: especially One Piece, Berserk and One-Punch Man.
Video games: 53 Platinum trophies on PlayStation, including Dark Souls, Elden Ring and The Witcher 3 (yes, I love it).