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On one G.I.Arkhipov’s theorem

https://doi.org/10.22405/2226-8383-2025-26-5-280-286

Abstract

In this paper in the model situation the generalized solution of the Cauchy problem of
linearalized the Corteveg – de Vriz equation are investigated. The solution are represented as
the Vinogradov’s trigonometric series, that permits to reduce the deduction to the Vinigradov’s method of the H.Weyl’s trigonometric sums.

About the Authors

Lyudmila Gennadievna Arkhipova
Lomonosov Moscow State University
Russian Federation


Vladimir Nikolaevich Chubarikov
Lomonosov Moscow State University
Russian Federation

doctor of physical and mathematical sciences, professor



References

1. Vinogradov, I. M. 1980, “Method of trigonometric sums in the number theory, 2nd edit.”, Moscow, Nauka, pp. 144.

2. Arkhipov, G. I., “Oskolkov, K. I. 1989, Special trigonometric series and their applications”, Math. Trans., 62,𝑁𝑜.2. pp. 145 – 155.

3. Oskolkov, K. I. 1989, “I.M.Vinogradov’s series and integrals and their applications”, Proc. MIAN., 190, pp. 186 – 221.

4. Oskolkov, K. I. 1991, “I.M.Vinogradov’s series in the Caushy problem for equations of Schr´odinger type”, Proc. MIAN., 200, pp. 265 – 288.

5. Karatsuba, A. A. 1983, “Basics of analytic number theory, 2nd edit”, Moscow, Nauka, pp. 240.

6. Chubarikov, V. N. 2015, “The elementary deduction of the estimate of the complete rational arithmetical sum from a polynomial”, Chebyshev Trans., V.16, № . 3(55), pp. 452 – 461.

7. Chubarikov, V. N. 2015, “The exponent of the convergence of the mean-value of complete rational arithmetical sums”, Chebyshev Trans., V.16, № . 4(56), pp. 303 – 318.

8. Chubarikov, V. N. 2016, “Arithmetical sums from values of a polynomial”, Dokl. RAS, V.466, № . 2, pp. 152 – 153.

9. Chubarikov, V. N. 2015, “Complete rational arithmetical sums”, Вull. Moscow. Univ. Ser.I, Math., mech., № . 1, pp. 60 – 61.

10. Gijasi, A. H., 2025, “Chubarikov, V. N. On Vinogradov’s series over prime numbers”, Chebyshev Trans., V.26, № . 3, pp. 81 – 95.

11. Arkhipov, G. I., Sadovnichii, V. A., Chubarikov, V. N. 2004, “Lectures on mathematical analysis: Text-book for higher educ. of Inst. 4th edit.”, M.: Drofa, P. 640.


Review

For citations:


Arkhipova L.G., Chubarikov V.N. On one G.I.Arkhipov’s theorem. Chebyshevskii Sbornik. 2025;26(5):280-286. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-5-280-286

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ISSN 2226-8383 (Print)