Gauss Sums, Kloosterman Sums, And Monodromy Groups
Gauss Sums, Kloosterman Sums, And Monodromy Groups
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发表时间：
1987
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通讯作者：
N. M. Katz
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作者：
N. M. Katz
对有限域上的指数和的研究，在近两个世纪前由高斯开始，近年来由于代数几何的进步而完全改变，最终在Deligne关于Weil猜想的工作中达到顶峰。它现在看来是一个非常有吸引力的混合代数几何，表示论，和层理论的化身等标准结构的经典分析卷积和傅立叶变换。这本书是同时帐户的一些这些想法，技术和结果，并考虑到他们的应用具体equidistribution问题有关Kloosterman和高斯总和。
The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.