## 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

## 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.## References

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## Additional Information

**Alan Adolphson**- Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
- MR Author ID: 23230
- Email: adolphs@math.okstate.edu
**Steven Sperber**- Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 165470
- Email: sperber@math.umn.edu
- 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: https://doi.org/10.1090/S0002-9947-03-03324-5
- MathSciNet review: 2020036