Zeros and coefficients
Alexandre Eremenko

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.
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Taxonomy
TopicsMeromorphic and Entire Functions · Aerospace Engineering and Control Systems · Mathematics and Applications
