Generalized Hypergeometric FunctionsHypergeometric 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. |
Contents
INTRODUCTION | 1 |
MULTIPLICATION BY X GAUSS CONTIGUITY | 15 |
ALGEBRAIC THEORY | 16 |
Copyright | |
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Common terms and phrases
a₁ a₂ algebraic analytic assertion assume B₁ C₁ Chapter choose coefficients commutative diagram completes the proof conclude condition Corollary deduce define definition denote det(I differential dimension dual Dwork element endomorphism equation exists factors finite follows g₁ gamma function gauss gauss sums H₁ H₂ hence hypergeometric functions hypothesis implies independent induces integral irreducible isomorphism Jacobi sums K₁ Laplace transform Lemma lies linear forms M₁ matrix monomials multiplication n₁ n₂ natural map notation operator ord(a p-adic p₁ polar locus Proposition R-sequence rational function reduced relative replaced resp right side ring S₁ S₂ satisfies 2.6 semigroup shows space subring subset surjective trivial u₁ Uk+i variables verify Ŵ₁ Wa-u write X₁ Y₁ zero θλι λ₁