Johann Verwee
PhD in Mathematics — Analytic & Probabilistic Number Theory
Computational methods / numerical experiments
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Email : mverwee (at) gmail [dot] com
Research interests
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 & 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
Publications
3. Effective Erdős-Wintner theorem for Cantor systems via a trailing-window method, International Journal of Number Theory (March 2026), published online.
2. Effective Erdős-Wintner theorems for digital expansions (with M. Drmota), Journal of Number Theory, 229 (December 2021), pages 218-260.
1. Effective Erdős-Wintner theorems (with G. Tenenbaum), Proc. Steklov Inst. Math., 314 (September 2021), pages 264-278.
Preprints
Preprints
6. Linear truncation on conditioned prime-factor fibres (March 2026).
5. A semigroup approach to iterated binomial transforms (January 2026).
4. Diagonal symmetrisation of tridiagonal Toeplitz matrices (January 2026).
3. A spectral product formula for repunits via a tridiagonal Toeplitz similarity (December 2025).
2. Nonasymptotic Quasi-Monte Carlo Bounds for Sobol' Indices: Bias via Discrepancy and Variance via a Large Sieve (October 2025).
1. Improvement of effective Erdős-Wintner theorem for Zeckendorf expansions (September 2025).
Under review / submitted
Under review / submitted
2. Short intervals for the Romanoff-type sumset (with Y. Ding), submitted (Februar 2026).
1. Erdős-Wintner theorem for linear recurrent bases, under review at Journal of Number Theory (January 2026).
In preparation
In preparation
1. Short-interval Bombieri-Vinogradov near level one for multiplicative functions of bounded modulus.
2. Erdős--Wintner theorem for quadratic Ostrowski numeration.
3. An Erdős-Wintner theorem on the fibre ω(n;E)=k for residue-class prime sets
4. Uniform Erdős--Wintner theorem in short intervals.
Talks
Talks
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
Curriculum Vitae
My CV is here.
Thesis & Master thesis
Thesis & Master thesis
Doctorate 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 & M. Drmota, defended on November 20, 2020.
Master thesis (in French): La fonction lambda de Liouville dans les petits intervalles
Under the direction of G. Tenenbaum, Université de Lorraine, 2016.
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