Föreläsning
Föreläsare
Jasson Vindas, Ghent University
Titel
Asymptotic distribution of Beurling’s generalized prime numbers
Tid
Kl13.30 - 14.15
Sammanfattning
This talk is a survey on classical and recent results concerning the asymptotic distri-bution of generalized prime numbers.The goal of Beurling's generalized prime number theory is to replace the ordinary prime numbers by a rather arbitrary non-decreasing sequence of positive real numbers (generalized primes), consider then the multiplicative semigroup generated by it (general-ized integers), and then establish relations between asymptotic properties of the counting functions of the generalized primes and integers. We will discuss various conditions that ensure the validity of the prime number theorem or the existence of an asymptotic density for the generalized integers.