Introduction to the Classical Theory of Abelian Functions (Translations of Mathematical Monographs) - Hardcover

Markushevich, A. I.

Hardcover

ISBN 10: 082184542X ISBN 13: 9780821845424

Publisher: Amer Mathematical Society, 1992

Synopsis

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.

About this title

Language Notes

Text: English (translation)
Original Language: Russian

Review

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

Very well suited for teaching and learning at the upper undergraduate level. -- Zentralblatt für Mathematik

Edition details

• Publisher: Amer Mathematical Society
• Publication date: 1992
• Language: English
• ISBN 10: 082184542X
• ISBN 13: 9780821845424
• Binding: Hardcover
• Number of pages: 175