An Introduction to the Theory of Multiply Periodic Functions by Frederick Baker
An Introduction to the Theory of Multiply Periodic Functions - Table of Contents
PART I. HYPERELLIPTIC FUNCTIONS OF TWO VARIABLES
1. Introductory
2. The Differential Equations for the Sigma Functions
3. Analytical Results Relating to the Associated Quartic Surfaces
4. The Expansion of the 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 Reduction of the Theory of a Multiply-Periodic Function to the Theory of Algebraic Functions
8. Defective Integrals
9. Propositions for Rational Functions; Expressions of a General Periodic Function by Theta Functions
10. The Zeros of the Jacobian Functions
What You Will Learn in An Introduction to the Theory of Multiply Periodic Functions
"An Introduction to the Theory of Multiply Periodic Functions" by "Henry F. Baker" is a text that lays the groundwork for understanding complex functions with more than one independent period. Although written in an older mathematical style, it remains a foundational resource for anyone studying the deeper structure of "algebraic curves", higher-genus surfaces, and their associated analytic functions.
Baker’s book introduces the theory of "hyperelliptic functions", multi-variable "theta functions", and related sigma and P-functions. He explains how these functions arise from integrals on Riemann surfaces and shows how multi-periodicity generalizes the familiar elliptic case. The text walks through power-series expansions, period relations, inversion problems, and the geometric meaning behind these analytic constructions.
While demanding in technical depth, the book’s influence is still felt in modern algebraic geometry, integrable systems, and the study of Abelian functions. Its blend of analysis and geometry makes it valuable for researchers seeking historical insight or a solid classical foundation. Despite its age, Baker’s systematic approach continues to shape our understanding of multi-periodic functions and their role in mathematics.
Book Details & Specifications
Title:
An Introduction to the Theory of Multiply Periodic Functions by Frederick Baker
Publisher:
University press
Year:
1907
Pages:
362
Type:
PDF
Language:
English
ISBN-10 #:
1164098977
ISBN-13 #:
978-1164098973
License:
Public Domain Work
Amazon:
Amazon
About the Author: Henry Frederick Baker
The author Henry Frederick Baker
(1866–1956) was a prominent British mathematician known for his deep work in "algebraic geometry", complex analysis, and the theory of Abelian functions. A long-time Cambridge scholar and Fellow of the Royal Society, he helped shape early 20th-century mathematical research through his clear, rigorous approach. Baker wrote several influential texts, including "An Introduction to the Theory of Multiply Periodic Functions", which showcases his expertise in advanced function theory and geometric methods. His work continues to influence modern studies of "Riemann surfaces" and "Abelian functions", marking him as a key figure in classical mathematical development.
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