Zeros and coefficients

TL;DR

This paper proves two theorems connecting the asymptotic distribution of zeros of analytic functions with their coefficients and the zeros of their derivatives.

Contribution

It introduces new theorems that relate the asymptotic behavior of zeros to coefficients and derivatives of analytic functions.

Findings

Zeros' distribution linked to coefficients' asymptotics

Zeros of functions and derivatives are asymptotically related

Provides theoretical foundation for analyzing zeros of analytic functions

Abstract

Two theorems on the asymptotic distribution of zeros of sequences of analytic functions are proved. First one relates the asymptotic behavior of zeros to the asymptotic behavior of coefficients. Second theorem establishes a relation between the asymptotic behaviors of zeros of a function and zeros of derivative.