Skip to main content
Log in

Estimation of a complete rational trigonometric sum. I

  • Published:
Mathematical Notes Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. V.I. Nechaev, “Estimate of a complete rational trigonometric sum,” Mat. Zametki,17, No. 6, 839–849 (1975).

    Google Scholar 

  2. S.B. Stechkin, “Estimate of a complete rational trigonometric sum,” Trudy Mat. Instituta Akad. Nauk SSSR,143, 188–207 (1977).

    Google Scholar 

  3. D.A. Mit'kin, “On the estimates and asymptotic formulas for rational trigonometric sums close to complete,” Mat. Sbornik,122(164) No. 4(12), 527–545 (1983).

    Google Scholar 

  4. G.I. Gusev and M.V. Kudryavtsev, An Isometric Linearization of Polynomials in p-adic Fields and Its Applications [in Russian], Saratov State University, Saratov, Dep. in VINITI on April 11, 1990, No. 2023-V90 (1990).

    Google Scholar 

  5. R.A. Smith, “Estimates for exponential sums,” Proc. Amer. Math. Soc.,79, No. 3, 365–368 (1980).

    Google Scholar 

  6. J.H. Loxton and R.A. Smith, “On Hua's estimate for exponential sums,” J. London Math. Soc. (2),26, No. 1, 15–19 (1982).

    Google Scholar 

  7. G.V. Chudnovskii, “Some analytic methods in the theory of transcendental functions,” Preprint, Inst. Math., No. 74-8, Ukr. SSR, Academy of Sciences, Kiev (1974).

    Google Scholar 

  8. J.H.H. Chalk, “On Hua's estimates for exponential sums,” Mathematika,34, 115–123 (1987).

    Google Scholar 

  9. M.V. Kudryavtsev, “On the number of solutions for the congruence f(x)≡0 (mod pα),” in: Constructive Methods and Algorithms of the Theory of Numbers, Abstracts of Reports at the All-Union School, Minsk, 10–16 September 1989, Minsk (1989).

  10. G. Sánder, Über die Anzahl der Lösungen einer Kongruenz,” Acta. Math.,87, No. 1, 13–17 (1952).

    Google Scholar 

  11. J.H.H. Chalk and R.A. Smith, “Sándor's theorem on polynomial congruences and Hensel's lemma,” Math. Reports, Acad. Sci. Canada,4, No. 1, 49–55 (1982).

    Google Scholar 

  12. A. Weil, “On some exponential sums,” Proc. Nat. Acad. Sci. USA,34, No. 5, 204–207 (1948).

    Google Scholar 

  13. J.H. Loxton and R.C. Vaughan, “The estimation of complete exponential sums,” Canad. Math. Bull.,28, No. 4, 440–454 (1985).

    Google Scholar 

  14. V.I. Nechaev and V.L. Topunov, “The estimation of the modulus of complete rational trigonometric sums of the third and fourth degrees,” Trudy Mat. Instituta Akad. Nauk SSSR,158, 125–129 (1981).

    Google Scholar 

  15. J.H.H. Chalk, “Quelque remarques sur les congruences polinómes modulo pα,” Comptes Rendus Acad. Sci., Ser. 1,307, No. 10, 513–515 (1988).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 53, No. 1, pp. 59–67, January, 1993.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kudryavtsev, M.V. Estimation of a complete rational trigonometric sum. I. Math Notes 53, 43–49 (1993). https://doi.org/10.1007/BF01208521

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01208521

Navigation