Some Properties of Zeros of the Umemura Polynomials of the Fifth Painlevé Equation

ABSTRACT We describe some properties of zeros of the Umemura polynomials associated with a class of rational solutions to the fifth Painlevé equation. A combinatorial formula for the discriminant of the Umemura polynomials is constructed. Based on the result, we investigate the multiplicity of zeros of the Umemura polynomials. We also present relations of Stieltjes type for the rational solutions. Further, we give a modest result for the maximal modulus of zeros of the Umemura polynomials.

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Journal
Studies in Applied Mathematics
Published
2025-09-01
DOI
https://doi.org/10.1111/sapm.70109
Primary Topic
Nonlinear Waves and Solitons
Type
article
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article

Some Properties of Zeros of the Umemura Polynomials of the Fifth Painlevé Equation

Tetsu Masuda
Studies in Applied Mathematics
Nonlinear Waves and Solitons
article

Some Properties of Zeros of the Umemura Polynomials of the Fifth Painlevé Equation

Tetsu Masuda
article en

Abstract

ABSTRACT We describe some properties of zeros of the Umemura polynomials associated with a class of rational solutions to the fifth Painlevé equation. A combinatorial formula for the discriminant of the Umemura polynomials is constructed. Based on the result, we investigate the multiplicity of zeros of the Umemura polynomials. We also present relations of Stieltjes type for the rational solutions. Further, we give a modest result for the maximal modulus of zeros of the Umemura polynomials.

Studies in Applied MathematicsVol. 155(3)
Aoyama Gakuin University (JP)
Openalex Percentile: Top 81%
Nonlinear Waves and Solitons
DOISourceOpenAlex
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Some Properties of Zeros of the Umemura Polynomials of the Fifth Painlevé Equation — Tetsu Masuda · Studies in Applied Mathematics (2025) | TGRS Research Map | TGRS