On the least type of entire functions of order \(\rho \in (0,1)\) with positive zeros (Q2830915)

The author discusses the theory of extremal problems in classes of entire functions with constraints on the growth and the distribution of zeros. Also she investigates problems associated with the completeness of exponential systems in complex domains. Further, she discusses the question of finding the exact lower bound for the types of all entire functions of an order belonging to the open interval \((0,1)\), whose zeros lie on a ray and have prescribed upper density and step in the light of order. Also, the author proves that the infimum is attained in this problem, and a detailed construction of the extremal function is given. This gives a complete solution of the extremal solution and generalizes a result of \textit{A. Yu. Popov} [Math. Notes 85, No. 2, 226--239 (2009); translation from Mat. Zametki 85, No. 2, 246--260 (2009; Zbl 1177.30037)].