Johann Verwee

activity

20202026

most citedEffective Erd\H os--Wintner theorems

1 citations · 1 across the 8 of their papers we have counts for

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math.NT2026

Terminal Blocks of Primes in Pisot Numeration Systems

Sungkon Chang, Johann Verwee

We prove a prime number theorem for fixed terminal block words in Pisot integer numeration systems. If the dominant root $φ$ is a Pisot number and the characteristic polynomial $P_…

math.NT2026

An Erdős-Wintner theorem for second-order linear recurrent bases

Johann Verwee

Let $a, b$ be integers with $1 \leq b \leq a$ , and let \[ G_0=1,\qquad G_1=a+1,\qquad G_{n+2}=aG_{n+1}+bG_n. \] For real-valued functions which are additive in the greedy $G$ -digits, we…

math.NT2026

Linear truncation for conditioned prime-factor fibres

Johann Verwee

In previous joint work with Tenenbaum, the truncation step $f \mapsto f_{R}$ in the conditional effective Erdos-Wintner theorem on the fibre $ω (n) = k$ yields, in the continuous case f…

math.NT2026

Short intervals for the Romanoff-type sumset

Yuchen Ding, Johann Verwee

Let $X$ be large and let $P$ denote the set of primes. Fix positive real parameters $r_{1}, \dots, r_{s}$ and a parameter $λ ⩾ 1$ determined by a balancing relation, and…

math.NT2025

Erdős-Wintner theorem for linear recurrent bases

Johann Verwee

Let $(G_{n})_{n ⩾ 0}$ be a linear recurrence sequence defining a numeration system and satisfying mild structural hypotheses. For real-valued G-additive functions (additive in…

math.NT2025

Improvement of effective Erdos-Wintner theorem for Zeckendorf expansions

Johann Verwee

We revisit the effective Erdos-Wintner theorem for Zeckendorf expansions. Drmota and the author obtained a uniform Kolmogorov bound whose error involves $T \sum_{j > L - 2 h} ∣ f (F_{j}) ∣$ , w…

math.NT2025

Effective Erdős--Wintner for Cantor numeration systems via a trailing-window method

Johann Verwee

We prove explicit Erdős--Wintner bounds for Cantor numeration systems via a simple trailing-window decomposition. We temporarily discard the last block of digits (the ``window'') a…

math.NT2020

Effective Erdős-Wintner theorems for digital expansions

Michael Drmota, Johann Verwee

In 1972 Delange observed in analogy of the classical Erd\H os-Wintner theorem that $q$ -additive functions $f (n)$ has a distribution function if and only if the two series $\sum f(d…

math.NT2020★ 1 cited

Effective Erd\H os--Wintner theorems

Gérald Tenenbaum, Johann Verwee

The classical theorem of Erd\H os \& Wintner furnishes a criterion for the existence of a limiting distribution for a real, additive arithmetical function. This work is devoted to…