A van der Corput lemma for the $p$-adic numbers
HTML articles powered by AMS MathViewer
- by Keith M. Rogers PDF
- Proc. Amer. Math. Soc. 133 (2005), 3525-3534 Request permission
Abstract:
We prove a version of van der Corput’s lemma for polynomials over the $p$-adic numbers.References
- G.I. Arhipov, A.A. Karacuba and V.N. Čubarikov, Trigonometric integrals, Math. USSR Izvestija 15 (1980), 211–239.
- E. Breuillard and T. Gelander, A topological Tits alternative, to appear, Ann. Math.
- Anthony Carbery, Michael Christ, and James Wright, Multidimensional van der Corput and sublevel set estimates, J. Amer. Math. Soc. 12 (1999), no. 4, 981–1015. MR 1683156, DOI 10.1090/S0894-0347-99-00309-4
- J.G. van der Corput, Zahlentheoretische abschätzungen, Math. Ann. 84 (1921), 53–79.
- Neal Koblitz, $p$-adic analysis: a short course on recent work, London Mathematical Society Lecture Note Series, vol. 46, Cambridge University Press, Cambridge-New York, 1980. MR 591682, DOI 10.1017/CBO9780511526107
- K. M. Rogers, Sharp van der Corput estimates and minimal divided differences, this issue.
- K. M. Rogers, Maximal averages along curves over the $p$-adic numbers, to appear, Bull. Austral. Math. Soc.
- Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993. With the assistance of Timothy S. Murphy; Monographs in Harmonic Analysis, III. MR 1232192
- M. H. Taibleson, Fourier analysis on local fields, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. MR 0487295
- J. Wright, $p$-Adic van der Corput lemmas, unpublished manuscript.
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
- Received by editor(s): August 30, 2003
- Received by editor(s) in revised form: July 8, 2004
- Published electronically: July 13, 2005
- Communicated by: Andreas Seeger
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3525-3534
- MSC (2000): Primary 43A70; Secondary 11F85
- DOI: https://doi.org/10.1090/S0002-9939-05-07919-0
- MathSciNet review: 2163587