T-adic exponential sums over finite fields

Chunlei Liu, Daqing Wan

Type: Article

Publication Date: 2009-11-09

Citations: 31

DOI: https://doi.org/10.2140/ant.2009.3.489

Abstract

We introduce T -adic exponential sums associated to a Laurent polynomial f .They interpolate all classical p m -power order exponential sums associated to f .We establish the Hodge bound for the Newton polygon of L-functions of T -adic exponential sums.This bound enables us to determine, for all m, the Newton polygons of L-functions of p m -power order exponential sums associated to an f that is ordinary for m = 1.We also study deeper properties of L-functions of T -adic exponential sums.Along the way, we discuss new open problems about the T -adic exponential sum itself.

Locations

Algebra & Number Theory - View - PDF
eScholarship (California Digital Library) - View - PDF
arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF
Project Euclid (Cornell University) - View - PDF

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Works Cited by This (64)

Action	Title	Year	Authors
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+ PDF Chat	Commutative algebra with a view toward algebraic geometry	1996	David Eisenbud
+	Linear algebraic groups	1966	Armand Borel
+	Commutative Ring Theory	1987	H. Matsumura
+	An introduction to G-functions	1994	Bernard Dwork Giovanni Gerotto Francis Sullivan
+	Representations of Algebraic Groups	2007	Jens Carsten Jantzen
+	Generic exponential sums associated to Laurent polynomials in one variable	2008	Chunlei Liu
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+	On the Connes-Kreimer construction of Hopf Algebras	1999	Ieke Moerdijk
+	Éléments de géométrie algébrique : III. Étude cohomologique des faisceaux cohérents, Seconde partie	1961	Alexander Grothendieck