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
• 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