Skip to main content
Log in

Five Lectures on the Life and Work of Academician I. M. Vinogradov

  • Research Articles
  • Published:
Proceedings of the Steklov Institute of Mathematics Aims and scope Submit manuscript

Abstract

The article reproduces the text of lectures on the life and work of the Soviet Academician I. M. Vinogradov, the first director of the Steklov Mathematical Institute of the Academy of Sciences of the USSR, delivered by his colleague and co-author A. A. Karatsuba (1937–2008) in September 1983 at the Tajik State University named after V. I. Lenin (now Tajik National University), Dushanbe.

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.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

References

  1. Ivan Matveevich Vinogradov: Biographical Materials on the Occasion of the 120th Anniversary of His Birth (RMP, Yaroslavl, 2011) [in Russian].

    Google Scholar 

  2. Pskov Province: List of Settlements according to Information from 1872–77, Ed. by V. Zverinskii (Central’nyi statisticheskii komitet Ministerstva vnutrennikh del, St. Petersburg, 1885), Lists of settlements of the Russian Empire, compiled and published by the Central Statistical Committee of the Ministry of Internal Affairs 34.

    Google Scholar 

  3. I. I. Vasil’ev, The Experience of the Geographic–Statistical Dictionary of the Pskov Province: Velikiye Luki District (Pskov. Gubern. Stat. Komitet, Pskov, 1884) [in Russian].

    Google Scholar 

  4. “Diocesan notices,” Pskov Diocesan Gazette. Official Part, No. 12 (June 15), 196 (1904).

    Google Scholar 

  5. “Diocesan notices,” Pskov Diocesan Gazette. Official Part, No. 10 (May 15), 163 (1904).

    Google Scholar 

  6. “Diocesan notices,” Pskov Diocesan Gazette. Official Part, No. 16 (Aug. 15), 263 (1904).

    Google Scholar 

  7. M. N. Huxley, “Exponential sums and lattice points. III,” Proc. London Math. Soc., Ser. 3, 87 (3), 591–609 (2003).

    Article  MathSciNet  Google Scholar 

  8. F. Chamizo and H. Iwaniec, “On the sphere problem,” Rev. Mat. Iberoam. 11 (2), 417–429 (1995).

    Article  MathSciNet  Google Scholar 

  9. D. R. Heath-Brown, “Lattice points in the sphere,” in Number Theory Progress, Vol. 2: Elementary and Analytic Number Theory (de Gruyter, Berlin, 1999), pp. 883–892.

    Google Scholar 

  10. T. D. Wooley, “The cubic case of the main conjecture in Vinogradov’s mean value theorem,” Adv. Math. 294, 532–561 (2016).

    Article  MathSciNet  Google Scholar 

  11. J. Bourgain, C. Demeter, and L. Guth, “Proof of the main conjecture in Vinogradov’s Mean Value Theorem for degrees higher than three,” Ann. Math., Ser. 2, 184 (2), 633–682 (2016).

    Article  MathSciNet  Google Scholar 

  12. A. A. Karacuba, “Sums of characters over prime numbers,” Math. USSR, Izv. 4 (2), 303–326 (1970) [transl. from Izv. Akad. Nauk SSSR, Ser. Mat. 34 (2), 299–321 (1970)].

    Article  Google Scholar 

  13. A. A. Karatsuba, “Arithmetic problems in the theory of Dirichlet characters,” Russ. Math. Surv. 63 (4), 641–690 (2008) [transl. from Usp. Mat. Nauk 63 (4), 43–92 (2008)].

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 314, pp. 5–30 https://doi.org/10.4213/tm4192.

Translated by E. Shubik and I. Nikitin

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karatsuba, A.A. Five Lectures on the Life and Work of Academician I. M. Vinogradov. Proc. Steklov Inst. Math. 314, 1–26 (2021). https://doi.org/10.1134/S0081543821040015

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0081543821040015

Navigation