On the algebraic independence of generic Painlevé transcendents

DOI10.1112/S0010437X13007525zbMath1309.14022arXiv1209.1562MaRDI QIDQ2877496

Joel Nagloo, Anand Pillay

Publication date: 22 August 2014

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.1562

zbMATH Keywords

model theoryPainlevé equationsalgebraic independencedifferentially closed fields

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) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (9)

Asymptotic behavior of the fourth Painlevé transcendents in the space of initial values ⋮ On transformations in the Painlevé family ⋮ Some functional transcendence results around the Schwarzian differential equation ⋮ Algebraic independence of generic Painlevé transcendents: PIII and PVI ⋮ Internality of logarithmic-differential pullbacks ⋮ Geometric triviality of the strongly minimal second Painlevé equations ⋮ Ax-Schanuel and strong minimality for the \(j\)-function ⋮ Corps différentiels et flots géodésiques I : Orthogonalité aux constantes pour les équations différentielles autonomes ⋮ When any three solutions are independent

Cites Work

• Algebraic Independence of Painlevé First Transcendents
• Solutions of the second and fourth Painlevé equations, I
• Classical solutions of the third Painlevé equation

This page was built for publication: On the algebraic independence of generic Painlevé transcendents