Abstract
A well-known extremal problem is considered: find the exact lower bound for all possible types of entire functions of the order \(\rho\in(1,\,+\infty)\setminus\mathbb{N}\) with roots on a ray, under the assumption that a lower density of roots is zero, and the upper one takes the given positive value. An approach to this problem is proposed. It based on the study indicator behavior of such entire functions. For the extremal value for any non-integer \(\rho>1\), the best known two-sided estimate is proved. Theoretical statements are supported by the results of numerical calculations.
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(Submitted by F. G. Avkhadiev)
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Braichev, G.G., Sherstyukov, V.B. On Indicator and Type of an Entire Function with Roots Lying on a Ray. Lobachevskii J Math 43, 539–549 (2022). https://doi.org/10.1134/S1995080222060075
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DOI: https://doi.org/10.1134/S1995080222060075