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An explicit estimate of exponential sums associated with a cubic polynomial

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References

  1. [1]

    J. H. Chalk and R. A. Smith, Sandor's Theorem on Polynomial Congruences and Hensel's Lemma,C. R. Math. Rep. Acad. Sci. Canada,4 (1982), 49–54.

  2. [2]

    P. Deligne, La conjecture de Weil,Publ. Math. IHES,43 (1974), 273–307.

  3. [3]

    R. Hartshorne,Algebraic Geometry, Springer Verlag (New York, Berlin, 1977), pp. 53–54.

  4. [4]

    N. Koblitz,p-adic Numbers, p-adic Analysis and Zeta Functions, Springer Verlag (New York, Berlin, 1977).

  5. [5]

    J. H. Loxton and R. A. Smith, Estimates for multiple exponential sums,J. Austral. Math. Soc.,33 (1982), 125–134.

  6. [6]

    J. H. Loxton and R. C. Vaughan, The estimation of complete exponential sums,Canad. Math. Bull.,28 (1985), 440–454.

  7. [7]

    K. A. M. Atan and J. H. Loxton, Newton polyhedra and solutions of congruences, inDiophantine Analysis, Ed. J. H. Lcxton and A. J. van der Poorten, London Math. Soc. Lecture Note Series 109 (Cambridge, 1986), pp. 67–82.

  8. [8]

    K. A. M. Atan, An estimate for multiple exponential sums in two variable.Sains Malaysiana,18 (1989), 129–135.

  9. [9]

    K. A. M. Atan, A method for determining the cardinality of the set of solutions to congruence equations,Pertaniko 11 (1988), 125–131.

  10. [10]

    K. A. M. Atan and I. B. Abdullah, On the estimate to solutions of congruence equations associated with a cubic form,Pertanika J. Sci. & Technol.,1 (1993), 1–10.

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Atan, K.A.M. An explicit estimate of exponential sums associated with a cubic polynomial. Acta Math Hung 69, 83–93 (1995). https://doi.org/10.1007/BF01874610

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Keywords

  • Explicit Estimate