Maximum modulus points of meromorphic functions and Valironʼs defect

The initial question of Paul Erdös concerned the existence of a non-polynomial entire function with the number of maximum modulus points tending to infinity. Later on the issue was considered also for meromorphic functions, leading to some interesting results on separated maximum modulus points and, in particular, their connection with Petrenkoʼs deviation and Valironʼs defect.