This final chapter is, naturally, concerned with the triumphant accomplishments of Poincaré: the creation of the theory of Fuchsian groups and automorphic functions. These developments brought together the theory of linear differential equations and the group-theoretic approach to the study of Riemann surfaces, so this account draws on all of the preceding material. It begins with a significant stage that is intermediate between the embryonic general theory and the developed Fuchsian theory: Lamé’s equation.


Singular Point Riemann Surface Elliptic Function Fuchsian Group Monodromy Group 
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© Birkhäuser Boston 2008

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