Anharmonic solutions to the Riccati equation and elliptic modular functions

DOI10.1515/forum-2017-0025zbMath1435.12004OpenAlexW2744237929MaRDI QIDQ1743451

Oumar Wone, Ahmed Sebbar

Publication date: 13 April 2018

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum-2017-0025

zbMATH Keywords

modular formsRiccati equationdifferential Galois theoryDarboux-Halphen systemDarboux polynomialtransvectantsCayley's processWedekind theorem

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Modular and automorphic functions (11F03) Differential algebra (12H05) Elliptic functions and integrals (33E05) Abstract differential equations (12H20) Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain (34M15)

Cites Work

• The 1-2-3 of modular forms. Lectures at a summer school in Nordfjordeid, Norway, June 2004
• On automorphisms of Enriques surfaces
• Transcendence of Jacobi's theta series
• Elementary First Integrals of Differential Equations
• The invariant theory of binary forms
• On Second Order Linear Differential Equations with Algebraic Solutions
• On Second Order Linear Differential Equations with Algebraic Solutions on Algebraic Curves
• On algebraic differential equations satisfied by automorphic functions
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