Exponential sums nondegenerate relative to a lattice

Adolphson, Alan; Sperber, Steven

doi:10.2140/ant.2009.3.881

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Exponential sums nondegenerate relative to a lattice

Alan Adolphson and Steven Sperber

Vol. 3 (2009), No. 8, 881–906

DOI: 10.2140/ant.2009.3.881

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

Vol. 3, No. 8, 2009