Vol. 3, No. 8, 2009

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Exponential sums nondegenerate relative to a lattice

Alan Adolphson and Steven Sperber

Vol. 3 (2009), No. 8, 881–906
Abstract

Our previous theorems on exponential sums often did not apply or did not give sharp results when certain powers of a variable appearing in the polynomial were divisible by p. We remedy that defect in this paper by systematically applying p-power reduction, making it possible to strengthen and extend our earlier results.

Keywords
exponential sums, $p$-adic cohomology
Mathematical Subject Classification 2000
Primary: 11L07
Secondary: 11T23, 14F30
Milestones
Received: 13 August 2008
Revised: 15 June 2009
Accepted: 2 August 2009
Published: 25 December 2009
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