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A van der Corput lemma for the  -adic numbers
Author(s):
Keith
M.
Rogers
Journal:
Proc. Amer. Math. Soc.
133
(2005),
3525-3534.
MSC (2000):
Primary 43A70;
Secondary 11F85
Posted:
July 13, 2005
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Additional information
Abstract:
We prove a version of van der Corput's lemma for polynomials over the  -adic numbers.
References:
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- 1.
- G.I. Arhipov, A.A. Karacuba and V.N. Cubarikov, Trigonometric integrals, Math. USSR Izvestija 15 (1980), 211-239.
- 2.
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- A. Carbery, M. Christ and J. Wright, Multidimensional van der Corput and sublevel set estimates, J. Amer. Math. Soc. 12 (1999), no. 4, 981-1015. MR 1683156 (2000h:42010)
- 4.
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- 5.
- N. Koblitz,
 -adic analysis: a short course on recent work, Cambridge Univ. Press, Cambridge, 1980. MR 0591682 (82c:12014) - 6.
- K. M. Rogers, Sharp van der Corput estimates and minimal divided differences, this issue.
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 -adic numbers, to appear, Bull. Austral. Math. Soc. - 8.
- E. M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Univ. Press, Princeton, NJ, 1993. MR 1232192 (95c:42002)
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- J. Wright,
 -Adic van der Corput lemmas, unpublished manuscript.
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Additional Information:
Keith
M.
Rogers
Affiliation:
School of Mathematics, University of New South Wales, Sydney, NSW 2052, Australia
Address at time of publication:
Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain
Email:
K.M.Rogers.99@cantab.net
DOI:
10.1090/S0002-9939-05-07919-0
PII:
S 0002-9939(05)07919-0
Keywords:
Van der Corput lemma,
$p$-adic,
oscillatory integrals
Received by editor(s):
August 30, 2003
Received by editor(s) in revised form:
July 8, 2004
Posted:
July 13, 2005
Communicated by:
Andreas Seeger
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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