Skip to main content
SpringerLink
Log in

Convergence Exponent of a Singular Series for a Multi–Dimensional Problem

  • Brief Communications
  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

The exponent of convergence of a singular series in the asymptotic formula for the number of solutions to a multidimensional problem is obtained.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. L M. Vinogradov, The Method of Trigonometric Sums in Number Theory (Nauka, Moscow, 1980) [in Russian].

    MATH  Google Scholar 

  2. L M. Vinogradov, Foundations of Number Theory, 10th Ed. (Lari', St. Petersburg, 2004) [in Russian].

    Google Scholar 

  3. L.–K. Hua, Selected Papers (Springer–Verlag, N.Y., 1983).

    MATH  Google Scholar 

  4. L.–K. Hua, The Method of Trigonometric Sums and its Applications to Number Theory (Mir, Moscow, 1964) [in Russian].

    Google Scholar 

  5. V. N. Chubarikov, “Convergence Exponent of a Singular Integral of One Many–Dimensional Additive Problem,” Doklady Rus. Akad. Nauk 46 (5), 530 (2015).

    Google Scholar 

  6. V. N. Chubarikov, “The Rate of Convergence of the Average Value of Full Rational Arithmetic Sums,” Chebyshev. Sborn. 16 (4(56)), 303 (2015).

    Google Scholar 

  7. G. L Arkhipov, A. A. Karatsuba, arid V. N. Chubarikov, Theory of Multiple Trigonometric Sums (Nauka, Moscow, 1987) [in Russian].

    MATH  Google Scholar 

  8. G. L Arkhipov, V. N. Chubarikov, and A. A. Karatsuba, Trigonometric Sums in Number Theory and Analysis. De Gruyter expositions in math. Vol. 39 (Berlin. N.Y., 2004).

  9. V. N. Chubarikov, “On a Multiple Trigonometric Integral,” Doklady Akad. Nauk SSSR 227 (6), 1308 (1976).

    MathSciNet  Google Scholar 

  10. V. N. Chubarikov, “Multiple Trigonometric Sums and Multiple Integrals,” Matem. Zametki 20 (1), 61 (1976).

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow State University, Moscow, 119991, Russia

    L. G. Arkhipova & V. N. Chubarikov

Authors
  1. L. G. Arkhipova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. N. Chubarikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. G. Arkhipova.

Additional information

Original Russian Text © L.G. Arkhipova and V.N. Chubarikov, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 13, No. 5, pp. 68–71.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arkhipova, L.G., Chubarikov, V.N. Convergence Exponent of a Singular Series for a Multi–Dimensional Problem. Moscow Univ. Math. Bull. 73, 207–209 (2018). https://doi.org/10.3103/S002713221805008X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S002713221805008X

Search

Navigation