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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Exponential sums on $\mathbf {A}^n$, II
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by Alan Adolphson and Steven Sperber PDF
Trans. Amer. Math. Soc. 356 (2004), 345-369 Request permission


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
  • MR Author ID: 23230
  • Email:
  • Steven Sperber
  • Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
  • MR Author ID: 165470
  • Email:
  • 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
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 345-369
  • MSC (2000): Primary 11L07, 11T23, 14F20, 14F30
  • DOI:
  • MathSciNet review: 2020036