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Averages in vector spaces over finite fields


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.

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[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.

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

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[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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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