Synopsis
In Lectures on the Theory of Elliptic Functions, Vol.
1, Hancock presents a rigorous look at elliptic functions and their algebraic structure. The text surveys how one-valued functions with algebraic addition-theorems fit into rational, simply periodic, and doubly periodic realms, building from foundational ideas to far-reaching consequences.
The book emphasizes key theorems and the logical path from general principles to concrete results, including Liouville’s theorem and Briot and Bouquet’s perspectives. It clarifies how elliptic functions connect to Riemann surfaces and how inversion problems are resolved within a unified framework.
- Follow the development of algebraic addition-theorems for elliptic and related functions.
- See how rational functions of multiple variables describe one-valued functions on complex surfaces.
- Learn how elliptic integrals arise from general expressions and their normal forms.
- Gain perspective on the classification of functions by their periodicity and algebraic properties.
Ideal for readers who want a thorough, historical, and theory-driven view of elliptic functions and their applications in complex analysis.
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