On the Least Type of an Entire Function of Order $\rho$ with Roots of a Given Upper $\rho$-Density Lying on One Ray

It is well known that the least possible type from the class of entire functions of prescribed order $\rho$ with upper root density 1 (for the exponent $\rho$) is $1/(e\rho)$. The author has proved that if all the roots of entire functions lie on one ray, then the situation is different: the least type for such a class on the set of orders $(1,+\infty)\setminus\mathbb N$ is distinct from zero and is bounded above.