Exponential sums and di?erential equations
Exponential sums and di?erential equations
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发表时间：
1990
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通讯作者：
N. M. Katz
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作者：
N. M. Katz
本书关注的是数学的两个领域，乍一看是不相关的，以及它们之间的一些类比和相互作用。这些领域是一个多项式系数的复变量线性微分方程理论，以及有限域上指数和的单参数族理论。在回顾了表示理论的一些结果之后，讨论了微分方程及其微分伽罗瓦群(G)和指数和的单参数族及其几何单群(G)的结果。本书的最后一部分专门讨论有关G和G在适当“对应”情况下的比较定理，这些比较定理为在超几何情况下“手工”发现的显著“巧合”提供了系统的解释。
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.