Date/heure
3 mars 2026
16:30 - 17:30
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Joni Teräväinen (University of Cambridge)
Catégorie d'évènement Colloquium
Résumé
We will discuss recent progress on several conjectures of Erdős and collaborators concerning the arithmetic function ω(n), including a conjecture of Erdős and Straus on long strings of integers with few prime factors, Erdős’s irrationality conjecture for a series involving ω(n), and the Erdős–Pomerance–Sárközy conjecture on the frequency of solutions to ω(n)=ω(n+1). A common theme is the interplay between probabilistic methods, sieves, and quantitative correlation estimates for multiplicative functions. I will outline how these tools allow us to resolve the first two conjectures and to verify the third for almost all values of x. This is based on joint work with Terence Tao.