Vol. 6, No. 3, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19, 1 issue

Volume 18, 12 issues

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
On unit root formulas for toric exponential sums

Alan Adolphson and Steven Sperber

Vol. 6 (2012), No. 3, 573–585
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.

Keywords
exponential sums, $A$-hypergeometric functions
Mathematical Subject Classification 2010
Primary: 11T23
Milestones
Received: 7 December 2010
Revised: 28 March 2011
Accepted: 8 May 2011
Published: 5 July 2012
Authors
Alan Adolphson
Department of Mathematics
Oklahoma State University
Stillwater, OK 74078
United States
Steven Sperber
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
United States