#### 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