The Riemann-Hilbert Problem

The Riemann-Hilbert problem (Hilbert's 21st problem) belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concerns the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this turned out to be a rare case of a wrong forecast made by him. In 1989 the second author (A. B.) discovered a counterexample, thus obtaining a negative solution to Hilbert's 21st problem in its original form.

Autorentext

Prof. Anosov und Prof. Bolibrukh sind beide am Steklov Institut in Moskau tätig.

Inhalt

Introduction - Counterexample to Hilbert's 21st problem - Irreducible representations - Miscellaneous topics - The case p 3 - Fuchsian equations.