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Estimates of Gaussian sums

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Literature cited

  1. 1.

    Z. I. Borevich and I. R. Shafarevich, Theory of Numbers [in Russian], Nauka, Moscow (1985).

  2. 2.

    I. M. Vinogradov, Foundations of Number Theory [in Russian], Nauka, Moscow (1981).

  3. 3.

    R. Lidl and H. Niederreiter, Finite Fields [Russian translation], Mir, Moscow (1988).

  4. 4.

    D. A. Mit'kin, “Estimates of rational trigonometric sums of special form,” Dokl. Akad. Nauk SSSR,224, 760–763 (1975).

  5. 5.

    A. Garcia and J. F. Voloch, “Fermat curves over finite fields,” J. Number Theory,30, 345–356 (1988).

  6. 6.

    S. B. Stechkin, “Estimation of Gaussian sums,” Mat. Zametki,17, No. 4, 579–588 (1975).

  7. 7.

    A. M. Odlyzko and R. P. Stanley, “Enumeration of power sums modulo a prime,” J. Number Theory,10, No. 2, 367–369 (1978).

  8. 8.

    N. M. Korobov, “Distribution of signs of periodic fractions,” Mat. Sb.,89, No. 4, 654–670 (1972).

  9. 9.

    H. Niederreiter, “On a problem of Kodama concerning the Hasse-Witt matrix and distribution of residues,” Proc. Jpn. Acad.,63, No. 9, 367–369 (1987).

  10. 10.

    I. E. Shparlinskii, “Properties of linear cyclic codes,” Probl. Peredachi Informatsii,19, 106–110 (1983).

  11. 11.

    A. A. Karatsuba, “Estimation of complete trigonometric sums,” Mat. Zametki,1, No. 2, 199–208 (1967).

  12. 12.

    I. E. Shparlinskii, “Rate of convergence of Newton iteration process and powers of certain codes,” Usp. Mat. Nauk,39, No. 2, 205–206 (1984).

  13. 13.

    I. E. Shparlinskii, “Systems of congruences,” in: Proceedings of the All-Union Conference on Discrete Mathematics. 1987 [in Russian], Moscow State Univ. (1989).

  14. 14.

    T. Khelleset, “Covering radius of linear cyclic and arithmetic codes,” Kibern. Sb.,25, 64–82 (1988).

  15. 15.

    I. E. Shparlinskii, “Estimation of certain sums with nonlinear recurring sequences,” in: Abstracts of Reports to the All-Union Conference “Theory of Transcendental Numbers and Its Applications” [in Russian], Moscow State Univ. (1983), pp. 168–169.

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Translated from Matematicheskie Zametki, Vol. 50, No. 1, pp. 122–130, July, 1991.

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Shparlinskii, I.E. Estimates of Gaussian sums. Mathematical Notes of the Academy of Sciences of the USSR 50, 740–746 (1991). https://doi.org/10.1007/BF01156612

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