Book:Hermann Weyl/The Concept of a Riemann Surface
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Hermann Weyl: The Concept of a Riemann Surface
Published $\text {1913}$, Dover Publications
- ISBN 0-486-47004-0 (translated by Hermann Weyl)
Subject Matter
Contents
- Preface
- I. Concept and Topology of Riemann Surfaces
- $\S 1$. Weierstrass' concept of an analytic function
- $\S 2$. The concept of an analytic form
- $\S 3$. The relation between the concepts "analytic function" and "analytic form"
- $\S 4$. The concept of a two-dimensional manifold
- $\S 5$. Examples of surfaces
- $\S 6$. Specialization; in particular, differentiable and Riemann surfaces
- $\S 7$. Orientation
- $\S 8$. Covering surfaces
- $\S 9$. Differentials and line integrals. Homology
- $\S 10$. Densities and surface integrals. The residue theorem
- $\S 11$. The intersection number
- II. Functions on Riemann Surfaces
- $\S 12$. The Dirichlet integral and harmonic differentials
- $\S 13$. Scheme for the construction of the potential arising from a doublet source
- $\S 14$. The proof
- $\S 15$. The elementary differentials
- $\S 16$. The symmetry laws
- $\S 17$. The uniform functions on $\mathfrak F$ as a subspace of the additive and multiplicative functions on $\hat {\mathfrak F}$. The Riemann-Roch theorem
- $\S 18$. Abel's theorem. The inversion problem
- $\S 19$. The algebraic function field
- $\S 20$. Uniformization
- $\S 21$. Riemann surfaces and non-Euclidean groups of motions. Fundamental regions. Poincaré $\Theta$-series
- $\S 22$. The conformal mapping of a Riemann surface onto itself
- Index