Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Koh, Doowon Shen, Chun-Yen and Shparlinski, Igor 2016. Averaging Operators Over Homogeneous Varieties Over Finite Fields. The Journal of Geometric Analysis, Vol. 26, Issue. 2, p. 1415.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 144, Issue 1
  • January 2008, pp. 13-27

Averages in vector spaces over finite fields

  • DOI:
  • Published online: 01 January 2008

We study the analogues of the problems of averages and maximal averages over a surface in when the euclidean structure is replaced by that of a vector space over a finite field, and obtain optimal results in a number of model cases.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]J. Bourgain , N. Katz and T. Tao . A sum-product estimate in finite fields, and applications, Geom. Funct. Anal. 14, no. 1 (2004), 2757.

[2]L. Carlitz and S. Uchiyama , Bounds for exponential sums, Duke Math. Jour. 24, (1957) 3741.

[3]M. Christ . Estimates for the k-plane transform. Indiana U. Math. J. 33, no. 6 (1984), 891910.

[5]P. Deligne . La conjecture de Weil, I. Inst. Hautes Etudes Sci. Publ. Math. 43 (1974), 273307.

[8]W. Schlag . On continuum incidence problems related to harmonic analysis. J. Funct. Anal. 201 2 (2003), 480521.

[9]A. Seeger . Degenerate Fourier integral operators in the plane. Duke Math. J. 71 (1993), 685745.

[11]T. Tao and J. Wright . Lp-improving estimates for averages along curves. J. Amer. Math. Soc 16 (2003), 605638.

[12]A. Weil . On some exponential sums. Proc. Nat. Acad. Sci. U.S.A 34 (1948), 204207.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *