Three open questions in the theory of Beurling's generalized primes

The goal of this researrch project is to make significant progress in the understanding of three
remarkable open problems about Beurling generalized primes and integers. These questions are
related to:
• The quest for a general abstract prime number theorem.
• The Malliavin second problem on the error term in the approximation of the asymptotic density of
Beurling generalized integers.
• Does the prime number theorem implies in general the mean-value vanishing of the Möbius
function?