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On several problems of the analytic number theory in the creative work of G. I. Arkhipov and S. M. Voronin

https://doi.org/10.22405/2226-8383-2021-22-2-7-26

Abstract

In the paper the formulation of problems are given and the contribution in their solution of the outstanding mathematicians of G. I. Arkhipov and S. M. Voronin are presented.
At the base of the paper two papers, which are written in the coonection with jubileum data of scientists, are put.

About the Authors

Vladimir Nikolaevich Chubarikov
Lomonosov Moscow State University
Russian Federation


Azar Khodabakhsh Ghyasi
Allameh Tabataba’i University
Islamic Republic of Iran

candidate of physical and mathematical sciences



References

1. G. I. Arkhipov, 2013, "Selected works" , Orel: Publishing house of Oryol. un-ta, 437 p.

2. G. I. Arkhipov., A. A. Karatsuba, 1979, "A new estimate of an integral of I. M. Vinogradov", Math.USSR-Izv. 13, P. 52-62.

3. G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, 1980, "Multiples of trigonometric sums", Tr. MIAN OF THE USSR, 151, P. 3–128.

4. G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, 1987, "The theory of multiple trigonometric sums" , M.: Nauka 370 p.

5. G. I. Arkhipov, V. A. Sadovnichii, V. N. Chubarikov, 1999, "Lectures on mathematical analysis.: Textbook for universities and pedagogical universities" , / Ed. V. A. Sadovnichii — Moscow: Higher School — 695 p.

6. G. I. Arkhipov, V. N. Chubarikov, 2011, "Sergey Mikhailovich Voronin (to the 65th anniversary of his birth)" , Chebyshevskii sbornik. vol. 12, issue 1, pp. 4–9.

7. S. M. Voronin, 1975, "Theorem on the “universality” of the Riemann zeta-function" , Math. USSR-Izv., 9, P. 443-453.

8. S. M. Voronin, 1978, "Prime numbers" , M.: Knowledge, 64 p.

9. S. M. Voronin, 1980, "On the zeros of some Dirichlet series lying on the critical line" , Izv.Akad.Nauk SSSR. Ser.Mat. 44, P.63-91.

10. S. M. Voronin, 1991, "About the method of I. M. Vinogradov", Number theory, algebra, mathematical analysis and their applications, Collection of articles Dedicated to the 100th

11. anniversary of the birth of Ivan Matveevich Vinogradov, Tr. MIAN, 200, Nauka, M., P. 114–123.

12. S. M. Voronin, 2006, "Selected works: Mathematics" , / Ed. A. A. Karatsuba — Moscow: Publishing House of the Bauman Moscow State Technical University, 480 p. — ISBN 5-7038-

13. -7.

14. S. M. Voronin, A. A. Karatsuba, 1994, "The Riemann Zeta function" , M.: Fizmatlit, 376 p. — ISBN 5–02–014120–8.

15. V. A. Sadovnichii, V. N. Chubarikov, 2007, "Gennady Ivanovich Arkhipov (on the 60th anniversary of his birth)" , Chebyshevskii sbornik, vol. 7, issue 1(17), P. 5–31.

16. G. I. Arkhipov, V. N. Chubarikov, A. A. Karatsuba, 2004, "Trigonometric sums in number theory and analysis" , de Gruyter Exp. Math., 39, Walter de Gruyter GmbH & Co. KG, Berlin,

17. x+554 pp.

18. S. M. Voronin, 1975, "Functional independence of Dirichlet L-functions" , Acta Arith., 27, P. 493-503.

19. A. A. Karatsuba, S. M. Voronin, 1992, "The Riemann Zeta-Function" , De Gruyter Exp. Math., 5, Walter de Gruyter CmbH&Co. KG, Berlin, x+396pp.


Review

For citations:


Chubarikov V.N., Ghyasi A.Kh. On several problems of the analytic number theory in the creative work of G. I. Arkhipov and S. M. Voronin. Chebyshevskii Sbornik. 2021;22(2):7-26. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-2-7-26

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