Theory of Functions of Complex Variable (Classic Reprint) - Softcover

Inhaltsangabe

<​ 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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