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2009 T-adic exponential sums over finite fields
Chunlei Liu, Daqing Wan
Algebra Number Theory 3(5): 489-509 (2009). DOI: 10.2140/ant.2009.3.489

Abstract

We introduce T-adic exponential sums associated to a Laurent polynomial f. They interpolate all classical pm-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 pm-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.

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Chunlei Liu. Daqing Wan. "T-adic exponential sums over finite fields." Algebra Number Theory 3 (5) 489 - 509, 2009. https://doi.org/10.2140/ant.2009.3.489

Information

Received: 3 March 2008; Revised: 8 January 2009; Accepted: 9 April 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1270.11123
MathSciNet: MR2578886
Digital Object Identifier: 10.2140/ant.2009.3.489

Subjects:
Primary: 11T23
Secondary: 11G25

Keywords: $L$-function , $T$-adic sum , exponential sum , Newton polygon

Rights: Copyright © 2009 Mathematical Sciences Publishers

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