Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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  • J. Wright, $p$-Adic van der Corput lemmas, unpublished manuscript.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 43A70, 11F85
  • Retrieve articles in all journals with MSC (2000): 43A70, 11F85
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