Generalized Hypergeometric Functions (Oxford Mathematical Monographs)

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.

'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