**Translations of Mathematical Monographs**

1992;
175 pp;
Softcover

MSC: Primary 14;
Secondary 33

**Print ISBN: 978-0-8218-4164-8
Product Code: MMONO/96.S**

List Price: $77.00

Individual Member Price: $61.60

# Introduction to the Classical Theory of Abelian Functions

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*A Markushevich*

The theory of Abelian functions, which was at the center of nineteenth-century mathematics, is again attracting attention. However, today it is frequently seen not just as a chapter of the general theory of functions but as an area of application of the ideas and methods of commutative algebra.

This book presents an exposition of the fundamentals of the theory of Abelian functions based on the methods of the classical theory of functions. This theory includes the theory of elliptic functions as a special case. Among the topics covered are theta functions, Jacobians, and Picard varieties. The author has aimed the book primarily at intermediate and advanced graduate students, but it would also be accessible to the beginning graduate student or advanced undergraduate who has a solid background in functions of one complex variable. This book will prove especially useful to those who are not familiar with the analytic roots of the subject. In addition, the detailed historical introduction cultivates a deep understanding of the subject. Thorough and self-contained, the book will provide readers with an excellent complement to the usual algebraic approach.

#### Readership

Upper level undergraduates, graduate students, and research mathematicians interested in analysis.

#### Reviews & Endorsements

Readers … will be grateful for this well-written modern account, which still preserves a historical perspective.

-- Bulletin of the London Mathematical Society

Very well suited for teaching and learning at the upper undergraduate level.

-- Zentralblatt MATH