This article is cited in 3 papers

On the Connection between the Growth of Zeros and the Decrease of Taylor Coefficients of Entire Functions

G. G. Braichev

Moscow State Pedagogical University

Abstract: In the theory of growth of entire functions, two trends have historically developed. The first trend deals with the calculation or estimation of the growth characteristics of the maximum modulus of an entire function (order, type, etc.) in terms of its Taylor series coefficients. In the second trend, the dependence of the growth of a function on the distribution of its zeros is studied. The aim of the present paper is to consider direct connections between the zeros and Taylor coefficients of an entire function, considering both classical and recent advances in the topic.

Keywords: upper and lower types of an entire function, zero sequence densities, Taylor coefficients.

UDC: 517.537.3

Received: 21.04.2022
Revised: 18.08.2022

DOI: 10.4213/mzm13559

 English version: Mathematical Notes, 2023, 113:1, 27–38

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