On the estimate $M(x)=o(x)$ for Beurling generalized numbers

Abstract

We show that the sum function of the Möbius function of a Beurling number system must satisfy the asymptotic bound $M(x)=o(x)$ if it satisfies the prime number theorem and its prime distribution function arises from a monotone perturbation of either the classical prime numbers or the logarithmic integral.

9 pages

References in corpus (4)

• On PNT equivalences for Beurling numbers
• Some examples in the theory of Beurling's generalized prime numbers
• A new generalized prime random approximation procedure and some of its applications
• Halász's theorem for Beurling generalized numbers