This nonfiction guide surveys automorphic and pseudo-automorphic functions, their behavior on Riemann surfaces, and how these ideas connect to differential equations. It offers a clear path through topics like surface connectivity, branch points, and the use of cross-cuts to understand multi-sheeted structures, all rooted in classical function theory.

What you’ll experience

Foundations of automorphic functions and their relations on a group of substitutions.
Ideas about Riemann surfaces, their connectivity, and how surfaces can be resolved into simply connected pieces.
Does and doesn’t of uniform functions, branch-points, and Schwarzian derivatives in context.
Examples from homoperiodic, triangular, and modular-function families to illustrate concepts.

Ideal for readers of advanced mathematics, the history of function theory, and those curious about how geometry and analysis meet in complex variables.

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