## A short course in automorphic functions |

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### Contents

Discontinuous Groups | 1 |

Automorphic Functions and Automorphic Forms | 66 |

Riemann Surfaces | 115 |

Copyright | |

1 other sections not shown

### Common terms and phrases

analytic angle assume automorphic form automorphic function bisectors boundary point C+{r called compact conjugate sides contains converges convex cusp forms cyclic group define denote differential of weight dimension Dirichlet series discontinuous group discrete group disk elliptic element equation euclidean Exercise finite number fixed circle fixed point follows Fourier coefficients free sides fundamental region fundamental set G_r(r genus Hence homeomorphism horocyclic hyperbolic area hyperbolic geometry infinite inner point integer intersect invariant isometric circle Lemma lies linear transformation lying mapping matrices meromorphic modular forms modular group multiple neighborhood normal polygon number of sides one-to-one open sets ordinary cycle ordinary point orthogonal parabolic cycle parabolic element parabolic vertex plane Poincare series point of H poles prove real discrete group Riemann surface scalar product sequence sides of N0 subgroup subset Suppose Theorem topology variable vector space vertices zero