742896
9780691085982
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This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably corresponding situations, which provide a systematic explanation of the remarkable coincidences found by hand in the hypergeometric case.Katz, Nicholas M. is the author of 'Exponential Sums and Differential Equations' with ISBN 9780691085982 and ISBN 0691085986.
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