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SHORT WEYL SUMS AND THEIR APPLICATIONS

https://doi.org/10.22405/2226-8383-2015-16-1-232-247

About the Authors

Z. Kh. Rakhmonov
Институт математики Академии наук Республики Таджикистан
Tajikistan


N. N. Nazrubloev
Институт математики Академии наук Республики Таджикистан
Tajikistan


A. О. Rakhimov
Институт математики Академии наук Республики Таджикистан
Tajikistan


References

1. Vaughan, R. C. 1981, "Some remarks in Weyl sums" , Colloquia Mathematica Societatis Janos Bolyai 34. Topics in classical number theory, Budapest, 1981, North Holland (1984), pp. 1585 – 1602.

2. Hua Loo-Keng 1964. "Method of Trigonometric Sums and Its Applications in Number Theory" , Nauka, Moscow, 190 p. (Russian translation); 1959. "Die Abschдtzung von Exponentialsummen und Ihre Anwendungen in der Zahlentheorie" , Teubner, Leipzig.

3. Vaughan, R. C. 1986, "On Waring’s problem for cubes" , J. f¨ur die reine und angewandte Math., vol. 365, pp. 122 – 170.

4. Rakhmonov, Z. Kh. & Shokamolova, J. A. 2009, "Short quadratic Weil’s exponential sums" , Izvestiya Akademii nauk Respubliki Tajikistan. Otdelenie fiziko-matematicheskikh, himicheskikh, geologicheskikh i tekhnicheskikh nauk, no. 2(135), pp. 7 – 18.

5. Rakhmonov, Z. Kh. & Mirzoabdugafurov, K. I. 2008, "About the estimations of short cube Weyl sums" , Doklady Akademii nauk Respubliki Tajikistan, vol. 51, no. 1, pp. 5 – 15.

6. Rakhmonov, Z. Kh., Azamov, A. Z. & Mirzoabdugafurov, K. I. 2010, "An estimate short exponential Weyl’s sums fourth degree" , Doklady Akademii nauk Respubliki Tajikistan, vol. 53, no. 10, pp. 737 – 744.

7. Rakhmonov, Z. Kh. 2014, "The Estermann cubic problem with almost equal summand" , Mathematical Notes, vol. 95, Issue 3 – 4, pp. 407 – 417. doi.org /10.1134/S0001434614030122.

8. Rakhmonov, Z. Kh. & Mirzoabdugafurov, K. I. 2008, "Waring’s problem for cubes with almost equal summands" , Doklady Akademii nauk Respubliki Tajikistan, vol. 51, no. 2, pp. 83 – 86.

9. Rakhmonov, Z. Kh. & Azamov, A. Z. 2011, "An asymptotic formula in Waring’s problem for fourth powers with almost equal summands" , Doklady Akademii nauk Respubliki Tajikistan, vol. 54, no. 3, pp. 34 – 42.

10. Rakhmonov, Z. Kh. & Ozodbekova, N. B. 2011, "An estimate short exponential Weyl’s sums" , Doklady Akademii nauk Respubliki Tajikistan, vol. 54, no. 4, pp. 257 – 264.

11. Rakhmonov, Z. Kh. 2013, "Short Weyl exponential sums" , Uchenye zapiski Orlovskogo gosudarstvennogo universiteta. Seriya estestvennie, tekhicheskie, meditsinskie nauki. no. 6, part 2, pp. 194 – 203.

12. Arkhipov, G. I., Chubarikov, V. N. & Karatsuba, A. A. 2004, "Trigonometric sums in number theory and analysis" , Berlin–New-York: Walter de Gruyter, 554 p.

13. Nazrubloev, N. N. 2014, "Mean value of the short Weyl fifth degree exponential sums" , Doklady Akademii nauk Respubliki Tajikistan, vol. 57, no. 7, pp. 531 – 537.

14. Nazrubloev, N. N. 2014, "Estimate of short Weyl sums of fifth degree on minor arcs" , Doklady Akademii nauk Respubliki Tajikistan, vol. 57, no. 9, pp. 710 – 716.

15. Karatsuba, A. A. & Korolev, M. A. 2007, "A theorem on the approximation of a trigonometric sum by a shorter one" , Izvestiya: Mathematics, 71(2), pp. 341 – 370, doi.org/10.1070/IM2007v071n02ABEH002359

16. Whittaker, E. F. & Watson, G. N. 1927, "A course of modern analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions . . . " Cambridge University Press.

17. Vaughan, R. C. 1981, The Hardy-Littlewood method, Cambridge Tracts in Mathematics, vol. 80, Cambridge University Press, Cambridge.


Review

For citations:


Rakhmonov Z.Kh., Nazrubloev N.N., Rakhimov A.О. SHORT WEYL SUMS AND THEIR APPLICATIONS. Chebyshevskii Sbornik. 2015;16(1):232-247. (In Russ.) https://doi.org/10.22405/2226-8383-2015-16-1-232-247

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