On Conjectures of A. Eremenko and A. Gabrielov
E. Mukhin, V. Tarasov
TL;DR
This paper proves a conjecture related to polynomials satisfying a specific differential equation involving a cubic polynomial h(x), advancing understanding in complex differential equations and polynomial behavior.
Contribution
It confirms a conjecture by Eremenko and Gabrielov regarding polynomials satisfying a particular second-order differential equation.
Findings
Proof of the conjecture by Eremenko and Gabrielov
Characterization of polynomials satisfying the differential equation
Insights into the structure of solutions involving cubic polynomials
Abstract
We study polynomials p(x) satisfying a differential equation of the form p"(x)-h'(x)p'(x)+H(x)p(x)=0, where h(x)=x^3/3+ax. We prove a conjecture of A. Eremenko and A. Gabrielov.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Differential Equations and Numerical Methods · Material Science and Thermodynamics