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Imperial Library
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Index
Cover
Title Page
Copyright Page
Dedication
Preface
Contents
I. Concept and Topology of Riemann Surfaces
§ 1. Weierstrass’ concept of an analytic function
§ 2. The concept of an analytic form
§ 3. The relation between the concepts “analytic function” and “analytic form”
§ 4. The concept of a two-dimensional manifold
§ 5. Examples of surfaces
§ 6. Specialization; in particular, differentiable and Riemann surfaces.
§ 7. Orientation
§ 8. Covering surfaces
§ 9. Differentials and line integrals. Homology
§ 10. Densities and surface integrals. The residue theorem
§ 11. The intersection number
II. Functions on Riemann Surfaces
§ 12. The Dirichlet integral and harmonic differentials
§ 13. Scheme for the construction of the potential arising from a doublet source
§ 14. The proof
§ 15. The elementary differentials
§ 16. The symmetry laws
§ 17. The uniform functions on as a subspace of the additive and multiplicative functions on The Riemann-Roch theorem
§ 18. Abel’s theorem. The inversion problem
§ 19. The algebraic function field
§ 20. Uniformization
§ 21. Riemann surfaces and non-Euclidean groups of motions. Fundamental regions. Poincaré Ө-series
§ 22. The conformal mapping of a Riemann surface onto itself . . .
Index
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