The Concept of a Riemann SurfaceCourier Corporation, 31. des. 2013 - 208 sider 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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a₁ Abel's theorem Abelian Abelian differential admissible local coordinate algebraic analytic continuation analytic form analytic function arbitrary associated boundary c₁ closed curve closed differential closed path coefficients compact concept conformal maps constant contained continuously differentiable convergence coordinate system countable cover transformations defined determined Dirichlet integral Dirichlet principle divisor domain E₁ equation equivalent Euclidean exists finite number fixed point follows function element Funktionen given grad harmonic function hence inequality integral function K₁ lattice linearly independent Math meromorphic functions multiples neighborhood obtain open set open unit disc parameter perfect covering surface plane poles power series proof punched surface radius regular analytic regular elements representation Riemann surface simply connected singularities smooth sphere surface F t-plane t₁ theorem theory topological map two-dimensional manifold uniformizing variable v₁ vanishes Weierstrass z-sphere z₁ zero