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The statistics of Weil's trigonometric sums

  • R. W. K. Odoni (a1)

Let F be the finite field of q = pn elements and let F0 be its prime subfield; thus, card F0 = p. For polynomials f ∈ F[x] and non-principal additive characters η of F A. Weil (1) proved the estimate

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(1)Weil, A. Sur les courbes algébriques, et les variétés qui s'en déduisent. Act. Sci. Indust. 1041 (Paris, Hermann, 1948).
(2)Stepanov, S. A.Bounds for Weil's sums, by elementary methods [Russian]. Izv. Akad. Nauk SSSR. Ser. Mat. 34 (1970), 10151037.
(3)Postnikov, A. G.Ergodic properties of measures in the theory of Diophantine approximation. Steklov Inst. Monograph, no. 82 (1966).
(4)Gnedenko, B. V.Theory of probability (Moscow, Mir, 1969).
(5)Bowman, F.Introduction to Bessel functions (Dover, New York, 1958), pp. 113114.
(6)Rayleigh, Lord. Collected papers (Cambridge University Press, 1920), vol. 6, 604626.
(7)Kluyver, J. C.A local probability problem. Proceedings of the Section of Science, Koningslijk Akad. van Wetensk. Amsterdam 8 (1906), 341350.
(8)Breiman, L.Probability (Addison-Wesley, 1968).
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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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