DEVELOPMENT OF THE VALIRON-LEVIN THEOREM ON THE LEAST POSSIBLE TYPE OF ENTIRE FUNCTIONS WITH A GIVEN UPPER ρ-DENSITY OF ROOTS

摘要

An entire function such that its roots have a given ρ-density and are located in an angle or on a ray is considered. For such a function, we solve the problem on the least possible type at order p. The case without assumptions about the location of the roots was considered by Valiron; the corresponding problem was completely solved by Levin.