Johann Verwee
PhD in Mathematics
Analytic and Probabilistic Number Theory
Effective Limit Theorems, Numeration Systems, and Prime Numbers
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Research interests
Research interests
Limit laws for arithmetic functions
Effective Erdős–Wintner theorems
Numeration systems and integer representations
Prime numbers in numeration systems
My research is mainly in analytic and probabilistic number theory. I am particularly interested in limit laws for arithmetic functions and their effective versions, especially in connection with the Erdős-Wintner theorem.
A substantial part of my work concerns numeration systems and arithmetic properties of integer representations in these systems, including Cantor and Zeckendorf numeration and, more generally, numeration systems associated with recurrence sequences.
My recent work also concerns problems involving prime numbers in numeration systems, in particular when conditions are imposed on digits or blocks of digits. These questions involve analytic and probabilistic methods, together with tools from automata, substitutions, and Rauzy fractals.
Publications
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 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.
Submitted manuscripts
Submitted manuscripts
An Erdős-Wintner theorem for second-order linear recurrent bases (August 2026).
Terminal blocks of primes in Pisot numeration systems (with S. Chang), October 2026.
Manuscripts in preparation
Manuscripts in preparation
Sums of two Zeckendorf--Niven numbers.
Longest target matches at sparse positions in binary expansions.
Research notes (not intended for publication)
Research notes (not intended for publication)
Linear truncation on conditioned prime-factor fibres (March 2026).
A semigroup approach to iterated binomial transforms (January 2026).
Diagonal symmetrisation of tridiagonal Toeplitz matrices (January 2026).
A spectral product formula for repunits via a tridiagonal Toeplitz similarity (December 2025).
Improvement of effective Erdős-Wintner theorem for Zeckendorf expansions (September 2025).
Talks and presentations
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.
Scientific service
Scientific service
Reviewer for Mathematical Reviews / MathSciNet (American Mathematical Society), since 2026.
Referee for Electronic Research Archive.
Supervision of a final-year student project at ENS Mines Nancy, 2020.
Co-organizer of the Journée de théorie des nombres, combinatoire additive et analyse de Fourier at Institut Élie Cartan de Lorraine (Nancy), June 15, 2018.
PhD and master's theses
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
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).
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