Generalized Hypergeometric Functions (Hardcover)

Bernard Dwork

ISBN 10: 0198535678 / ISBN 13: 9780198535676

Published by Oxford University Press, Oxford, 1990

About this Item

Hardcover. Hypergeometric functions have occupied a significant position in mathematics for over two centuries. This monograph, by one of the foremost experts, is concerned with the Boyarsky principle which expresses the analytical properties of a certain proto-gamma function. Professor Dwork develops here a theory which is broad enough to encompass several of the most important hypergeometric functions in the literature and their cohomology. A centraltheme is the development of the Laplace transform in this context and its application to spaces of functions associated with hypergeometric functions. Consequently, this book represents a significantfurther development of the theory and demonstrates how the Boyarsky principle may be given a cohomological interpretation. The author includes an exposition of the relationship between this theory and Gauss sums and generalized Jacobi sums, and explores the theory of duality which throws new light on the theory of exponential sums and confluent hypergeometric functions. Hypergeometric functions have occupied a significant position in mathematics for over two centuries. This monograph is concerned with the Boyarsky principle which expresses the analytic properties of a certain proto-gamma function. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9780198535676

Bibliographic Details

• Title: Generalized Hypergeometric Functions (Hardcover)
• Publisher: Oxford University Press, Oxford
• Publication Date: 1990
• Language: English
• ISBN 10: 0198535678
• ISBN 13: 9780198535676
• Binding: Hardcover
• Condition: new

About this title

Synopsis

Hypergeometric functions have occupied a significant position in mathematics for over two centuries. This monograph, by one of the foremost experts, is concerned with the Boyarksy principle which expresses the analytic properties of a certain proto-gamma function. The author develops a theory which is broad enough to encompass several of the most important hypergeometric functions in the literature and their cohomology. A central theme is the development of the Laplace transform in this context and its application to spaces of functions associated with hypergeometric functions. Consequently, this book represents a significant further development of the theory and demonstrates how the Boyarksy principle may be given a cohomological interpretation. The author includes an exposition of the relationship between this theory and Gauss sums and generalized Jacobi sums, and explores the theory of duality which throws new light on the theory of exponential sums and confluent hypergeometric functions.

Review

'The subject is treated from a sophisticated viewpoint appropriate for developing the arithmetic and geometric aspects of the theory of which the author is a renowned exponent. The book is wide ranging ... most interesting and informative, and clearly it is a 'must' for anyone with research interests in this general area of algebraic geometry and number theory.' C.F. Woodcock, London Mathematical Society