Date/heure
5 mai 2022
14:30 - 15:30
Lieu
Salle Döblin
Oratrice ou orateur
Andreas Weingartner (Southern Utah University, États-Unis)
Catégorie d'évènement Analyse et théorie des nombres
Résumé
Given an arithmetic function $\theta$, we consider the set
$$ \mathcal{B}_\theta = \Bigl\{n\ge 1: p|n \Rightarrow p\le \theta\Bigl(\prod_{q<p \atop q^\alpha || n} q^\alpha \Bigr) \Bigr\},$$
where $p$ and $q$ denote primes. Depending on the choice of $\theta$, the possible sets $\mathcal{B}_\theta$ include the set of prime powers, almost primes, friable numbers, dense numbers, and practical numbers.
We will discuss (1) asymptotic results for the counting function of $\mathcal{B}_\theta$, (2) a generalization of the Siegel-Walfisz theorem, and (3) the normal order of the number of prime factors of integers in $\mathcal{B}_\theta$.