The problem on the minimal type of entire functions of order $\rho\in(0,1)$ with positive zeroes of prescribed densities and step

Abstract

We consider the problem on the least possible type of entire functions of order $\rho\in(0,1)$, whose zeroes lie on a ray and have prescribed densities and step. We prove the exactness of the estimate obtained previously by the author for the type of these functions. We provide a detailed justification for the construction of the extremal entire function in this problem.