Fuchsian equation

A Fuchsian (differential) equation is a linear homogeneous ordinary differential equation with analytic coefficients in the complex domain whose all singular points are regular singular points. In other words, it is the 1-dimensional case of the theory of meromorphic differential equations with only regular singular points. Riemann 21st problem is concerned with finding a Fuchsian equation with prescribed points of singularities and prescribed monodromies. The corresponding connection is also called Fuchsian.

  • M.V. Fedoryuk, Fuchsian equation, Springer online Enc. of Math.

  • J.L. Fuchs, J. Reine Angew. Math. 66, 121–160 (1866); 68, 354–385 (1868)

  • A. Hefliger, Local theory of meromorphic connections in dimension one (Fuchs theory), pages 129-149 of “Algebraic D-modules”, A. Borel, ed.

  • P. Deligne, Équations différentielles à points singuliers réguliers, Lect. Notes in Math. 163, Springer-Verlag (1970)

Revised on March 25, 2010 20:06:56 by Zoran Škoda (