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< b>Explore the geometry behind automorphic functions and Riemann surfaces.
This advanced text connects complex analysis with geometric insight, showing how automorphic functions behave on multi‑sheeted surfaces and how their equations reveal deep structure. This edition surveys how Riemann’s ideas apply to uniform functions of position, the role of branch-points and coverings, and how differential equations arise from automorphic theory. It also introduces the canonical forms, connectivity, and resolution methods that help visualize multi‑valued functions on complex surfaces.
- How automorphic functions relate to their algebraic relations and to Schwarzian derivatives.
- The construction and connectivity of Riemann surfaces, including branch-points, sheets, and cross-cuts.
- How to express complex functions on these surfaces and understand their differential equations of higher order.
- Canonical forms, ramification, and the link between geometric structure and analytic behavior.
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Theory of Functions of a Complex Variable (Classic Reprint)
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Paperback. Zustand: New. Print on Demand. This book is a detailed discussion of the theory of functions of a complex variable, based on the works of Weierstrass, Mittag-Leffler, Riemann, and others. It begins with the basic concepts of functions, their representations in terms of series and derivatives, and their properties under conformal transformations. The book then delves into uniform functions, multiform functions, Riemann surfaces, and algebraic functions, providing a thorough understanding of the connections between them. The author also explores transcendental integral functions, functions with essential singularities, and functions with unlimited essential singularities. The text includes examples and exercises throughout to illustrate the concepts and their applications. This book offers a comprehensive and rigorous treatment of the theory of functions of a complex variable, suitable for mathematics students and researchers interested in this field. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Bestandsnummer des Verkäufers 9781440070334_0
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Theory of Functions of Complex Variable Classic Reprint
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Theory of Functions of Complex Variable Classic Reprint
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Theory of Functions of a Complex Variable (Classic Reprint)
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Paperback. Zustand: Brand New. 706 pages. 9.00x6.00x1.59 inches. This item is printed on demand. Bestandsnummer des Verkäufers zk1440070334
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