Journal of the
Korean Mathematical Society JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008
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J. Korean Math. Soc.

Published online April 5, 2022

Copyright © The Korean Mathematical Society.

A Note on the Zeros of Jensen Polynomials

Young-One Kim and Jungseob Lee

Seoul National University, Ajou University

Abstract

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Sufficient conditions for the Jensen polynomials of the
derivatives of a real entire function to be hyperbolic are obtained.
The conditions are given in terms of the growth rate and zero
distribution of the function. As a consequence some recent results
on Jensen polynomials, relevant to the Riemann hypothesis, are
extended and improved.

Keywords: Zeros of polynomials and entire functions, Jensen polynomials, Riemann hypothesis

MSC numbers: 30C15, 30D15

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