Liouville's theorem on integration in finite terms for \(\mathrm{D}_\infty , \mathrm{SL}_2\), and Weierstrass field extensions

DOI10.1007/s00013-023-01907-5arXiv2308.00659OpenAlexW4386743895MaRDI QIDQ6077852

Partha Kumbhakar, Varadharaj Ravi Srinivasan

Publication date: 27 September 2023

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2308.00659

zbMATH Keywords

Liouville's theoremdifferential fieldsPicard-Vessiot extensionsWeierstrass differential equation

Mathematics Subject Classification ID

Elliptic curves (14H52) Differential algebra (12H05) Field extensions (12F99)

Cites Work

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• An algorithm for solving second order linear homogeneous differential equations
• Autonomous functions
• On Liouville's theory of elementary functions
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• Integration in finite terms with elementary functions and dilogarithms
• Liouville's theorem on functions with elementary integrals
• An Extension of Liouville’s Theorem on Integration in Finite Terms
• Geometric characterization of strongly normal extensions
• Galois Theory of Differential Fields

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