Some examples in the theory of Beurling's generalized prime numbers

Abstract

Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.

26 pages

Cited by in corpus (7)

• On PNT equivalences for Beurling numbers
• Beurling integers with RH and large oscillation
• Distribution of Beurling primes and zeroes of the Beurling zeta function I. Distribution of the zeroes of the zeta function of Beurling
• A Riemann-von Mangoldt-type formula for the distribution of Beurling primes
• An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions
• On the estimate $M(x)=o(x)$ for Beurling generalized numbers
• $M(x)=o(x)$ Estimates for Beurling numbers