Asymptotic Variation of Sheaves of One-variable Exponential Sums
نویسنده
چکیده
In this paper we prove that there exists a Zariski dense open subset U defined over Q in the parameter space of one-variable rational functions with prescribed l poles with fixed orders, such that for every geometric point f in U(Q), the L-function of exponential sum of f at p has Newton polygon approaches the Hodge polygon as p approaches infinity. This result generalizes some result in [13] and [14]. We also give a new transformation theorem which generalizes a theorem of Wan in [9].
منابع مشابه
Exponential sums over finite fields, II: introduction to cohomological methods
Contents Chapter 1. Introduction 1 1. Why is the one-variable theory not sufficient? 1 2. Outline of the rest of the book 1 Chapter 2. Background material: algebraic geometry 3 1. Affine algebraic varieties 3 2. First examples 7 3. Computing with algebraic varieties 7 Chapter 3. Summands for algebraic exponential sums 8 1. From Dirichlet characters to Galois characters 8 2. From Galois groups t...
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