Complex Analysis on Riemann Surfaces
by Curtis McMullen
Publisher: Harvard University 2005
Number of pages: 89
Contents: Maps between Riemann surfaces; Sheaves and analytic continuation; Algebraic functions; Holomorphic and harmonic forms; Cohomology of sheaves; Cohomology on a Riemann surface; Riemann-Roch; Serre duality; Maps to projective space; Line bundles; Curves and their Jacobians; Hyperbolic geometry; Quasiconformal geometry.
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by G.E. Fisher, I.J. Schwatt - Philadelphia G.E. Fisher
Contents: Geometric representation of imaginary quantities; Functions of a complex variable in general; Multiform functions; Integrals with complex variables; General properties of functions; Infinite and infinitesimal values of functions; etc.
by Leif Mejlbro - BookBoon
This is an introductory book on complex functions theory. From the table of contents: Introduction; The Complex Numbers; Basic Topology and Complex Functions; Analytic Functions; Some elementary analytic functions; Index.
by R. B. Ash, W. P. Novinger - Dover Publications
The text for advanced undergraduates and graduates, it offers a concise treatment, explanations, problems and solutions. Topics include elementary theory, general Cauchy theorem and applications, analytic functions, and prime number theorem.
by H. Maass - Tata institute of Fundamental Research
This is an elementary introduction to the theory of modular functions and modular forms. Basic facts from the theory of functions of a complex variable and some properties of the elementary transcendental functions are the only prerequisites.