Mathematics

On some metric characteristics of the entire functions that connected with the model function of growth

M. V. Kabanko

Kursk State University, Kursk, Russia

Abstract: The concept of proximate order is widely used in the theories of integer, meromorphic, subharmonic, and plurisubharmonic functions. In this paper, we provide a general interpretation of this concept as a proximate order relative to the model growth function. The classical proximate order in the sense of Valiron is the particular case of proximate order relative to the model growth function. The main result of this work is a lower estimate of the distance between the points at which the maximum modulus of the entire function and the set of zeros of this function is reached, using the concept of a proximate order relative to the model function.

Keywords: model function, growth function, proximate order, convex function, entire function.

UDC: 517.53

Received: 27.12.2024
Revised: 26.07.2025

DOI: 10.47475/2500-0101-2025-10-4-677-687