Geodesic
On the Least Type of an Entire Function of Order~$\rho$ with Roots of a Given Upper $\rho$-Density Lying on One Ray
Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 246-260.

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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.
Keywords: entire function, least type of an entire function, upper density of a sequence, Lindelöf theorem. 
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A. Yu. Popov. On the Least Type of an Entire Function of Order~$\rho$ with Roots of a Given Upper $\rho$-Density Lying on One Ray. Matematičeskie zametki, Tome 85 (2009) no. 2, pp. 246-260. http://geodesic.mathdoc.fr/item/MZM_2009_85_2_a7/

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