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Seminarie i matematik

Asymptotic distribution of Beurling’s generalized prime numbers

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.

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