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Development of the Valiron–Levin Theorem on the Least Possible Type of Entire Functions with a Given Upper ρ-Density of Roots

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Abstract

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 ρ. The case without assumptions about the location of the roots was considered by Valiron; the corresponding problem was completely solved by Levin.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    A. Yu. Popov

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  1. A. Yu. Popov
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Correspondence to A. Yu. Popov.

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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 49, Proceedings of the Crimean Autumn Mathematical School-Symposium, 2013.

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Popov, A.Y. Development of the Valiron–Levin Theorem on the Least Possible Type of Entire Functions with a Given Upper ρ-Density of Roots. J Math Sci 211, 579–616 (2015). https://doi.org/10.1007/s10958-015-2618-8

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  • DOI: https://doi.org/10.1007/s10958-015-2618-8

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