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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Exponential sums on $\mathbf{A}^n$, II


Authors: Alan Adolphson and Steven Sperber
Journal: Trans. Amer. Math. Soc. 356 (2004), 345-369
MSC (2000): Primary 11L07, 11T23, 14F20, 14F30
Published electronically: May 29, 2003
MathSciNet review: 2020036
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Abstract: We prove a vanishing theorem for the $p$-adic cohomology of exponential sums on $\mathbf{A}^n$. In particular, we obtain new classes of exponential sums on $\mathbf{A}^n$ that have a single nonvanishing $p$-adic cohomology group. The dimension of this cohomology group equals a sum of Milnor numbers.


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Additional Information

Alan Adolphson
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: adolphs@math.okstate.edu

Steven Sperber
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: sperber@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03324-5
PII: S 0002-9947(03)03324-5
Keywords: Exponential sum, $p$-adic cohomology, $l$-adic cohomology
Received by editor(s): May 29, 2002
Received by editor(s) in revised form: February 13, 2003
Published electronically: May 29, 2003
Additional Notes: The first author was supported in part by NSA Grant MDA904-97-1-0068 and NSF Grant DMS-0070510
Article copyright: © Copyright 2003 American Mathematical Society