Algebraic independence of generic Painlevé transcendents: PIII and PVI

DOI10.1112/blms.12309zbMath1444.14065arXiv1708.02962OpenAlexW3100151499MaRDI QIDQ5110603

Joel Nagloo

Publication date: 21 May 2020

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.02962

zbMATH Keywords

Painlevé equationRiccati equationalgebraic independence conjecture

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Relationships between algebraic curves and integrable systems (14H70)

Related Items (3)

Generic differential equations are strongly minimal ⋮ A classification of first order differential equations ⋮ When any three solutions are independent

Cites Work

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• On algebraic relations between solutions of a generic Painlevé equation
• Algebraic solutions of the sixth Painlevé equation
• An algorithm for solving second order linear homogeneous differential equations
• Studies of the Painlevé equations. I: Sixth Painlevé equation \(P_{VI}\)
• On the algebraic independence of generic Painlevé transcendents
• Picard-Vessiot Extensions of Real Differential Fields
• Algebraic Independence of Painlevé First Transcendents
• Solutions of the third Painlevé equation I
• Classical solutions of the third Painlevé equation
• Local and Global Aspects of Lie's Superposition Theorem

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