Università degli Studi di Cagliari
Conferenza “Asymptotic distribution of Beurling's generalized primes” a cura del dott. Jasson VINDAS (Ghent University, Belgio)
13 febbraio 2012
Conferenza “Asymptotic distribution of Beurling’s generalized primes” a cura del dott. Jasson VINDAS (Ghent University, Belgio)
Lunedi 13 febbraio 2012 - alle ore 11.15, nell’Aula D del Dipartimento di matematica e Informatica - nell’ambito delle attività di ricerca e dei programmi di internazionalizzazione, il Dipartimento e il Dottorato di ricerca di matematica e calcolo scientifico organizzano la conferenza
Asymptotic distribution of Beurling’s generalized primes
a cura del visiting professor
Dottor Jasson VINDAS (Ghent University, Belgio)
ABSTRACT
This talk is a non-technical survey on classical and recent results concerning the asymptotic distribution of Beurling’s generalized primes. 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
This talk is a non-technical survey on classical and recent results concerning the asymptotic distribution of Beurling’s generalized primes. 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 (generalized integers), and then establish relations between asymptotic properties of the counting functions of generalized primes and integers. We will discuss various conditions that ensure
the validity of the prime number theorem. Interestingly, in the context of generalized number systems, the prime number theorem is not always true. It is therefore natural to ask whether at least Chebyshev type estimates are satisfied, we will also address the problem of finding conditions that guarantee such estimates.
INFO
Prof. Ph.D. Todor V. Gramtchev
Dipartimento di Matematica e Informatica
tel./fax: 070.675.85.34/04 - email: todor@unica.it
(ic)