Multiply Periodic Functions
2nd Edition
Published on 1. June 2020
Book
Paperback/Softback
350 pages
978-0-521-54648-5 (ISBN)
Description
This is a re-issue of the classic book from H. F. Baker. In two parts, this book first deals with the theory of hyperelliptic functions of two variables, and then with the reduction of the theory of general multiply-periodic functions to the theory of algebraic functions. It provides an elementary and self-contained introduction to many of the leading ideas in the theory of multiply periodic functions, whilst illuminating the importance of this theory in analytical geometry.
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Content
Part I. Hyperelliptic Functions of Two Variables: 1. Introduction; 2. The differential equations for the sigma functions; 3. Analytical results relating to the associated quartic surfaces; 4. The expansion of sigma functions; 5. Certain functional relations and their geometrical interpretation; Part II. The Reduction of the Theory of Multiply-Periodic Functions to the Theory of Algebraic Functions: 6. General introductory theorems; 7. On the rreduction of the theory of a multiply-periodic function to the theory of algebraic functions; 8. Defective integrals; 9. Propositions for rational functions. Expression of a general periodic function by theta functions; 10. The zeros of Jacobian functions.