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2012 On unit root formulas for toric exponential sums
Alan Adolphson, Steven Sperber
Algebra Number Theory 6(3): 573-585 (2012). DOI: 10.2140/ant.2012.6.573

Abstract

Starting from a classical generating series for Bessel functions due to Schlömilch, we use Dwork’s relative dual theory to broadly generalize unit-root results of Dwork on Kloosterman sums and Sperber on hyperkloosterman sums. In particular, we express the (unique) p-adic unit root of an arbitrary exponential sum on the torus Tn in terms of special values of the p-adic analytic continuation of a ratio of A-hypergeometric functions. In contrast with the earlier works, we use noncohomological methods and obtain results that are valid for arbitrary exponential sums without any hypothesis of nondegeneracy.

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Alan Adolphson. Steven Sperber. "On unit root formulas for toric exponential sums." Algebra Number Theory 6 (3) 573 - 585, 2012. https://doi.org/10.2140/ant.2012.6.573

Information

Received: 7 December 2010; Revised: 28 March 2011; Accepted: 8 May 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1251.11081
MathSciNet: MR2966711
Digital Object Identifier: 10.2140/ant.2012.6.573

Subjects:
Primary: 11T23

Keywords: $A$-hypergeometric functions , exponential sums

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.6 • No. 3 • 2012
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