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Concept of a Riemann Surface.

Author: Hermann Weyl
Publisher: Dover Publications, 2013.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology. The author intended this book not only to develop the basic  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Hermann Weyl
ISBN: 1306341248 9781306341240 9780486131672 048613167X
OCLC Number: 868271486
Description: 1 online resource
Contents: 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.

Abstract:

This classic on the general history of functions was written by one of the twentieth century's best-known mathematicians. Hermann Weyl, who worked with Einstein at Princeton, combined function theory and geometry in this high-level landmark work, forming a new branch of mathematics and the basis of the modern approach to analysis, geometry, and topology. The author intended this book not only to develop the basic ideas of Riemann's theory of algebraic functions and their integrals but also to examine the related ideas and theorems with an unprecedented degree of rigor. Weyl's two-part treatment begins by defining the concept and topology of Riemann surfaces and concludes with an exploration of functions of Riemann surfaces. His teachings illustrate the role of Riemann surfaces as not only devices for visualizing the values of analytic functions but also as indispensable components of the theory.

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