Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2022; 59(4): 775-787

Published online July 1, 2022 https://doi.org/10.4134/JKMS.j210622

Copyright © The Korean Mathematical Society.

A note on the zeros of Jensen polynomials

Young-One Kim, Jungseob Lee

Seoul National University; Ajou University

Abstract

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: Primary 30C15, 30D15

Supported by: The first author was supported by the SNU Mathematical Sciences Division for Creative Human Resources Development.

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