Advertisement

Programming and Computer Software

, Volume 44, Issue 2, pp 100–104 | Cite as

Algorithm for Constructing an Analog of Plan’s Formula

  • V. I. Kuzovatov
  • A. A. Kytmanov
Article
First Online:
Received:
  • 31 Downloads

Abstract

We present an algorithm for constructing an analog of Plan’s formula, which is essential in obtaining a functional relation to the classical Riemann zeta-function. The algorithm is implemented in the Maple computer algebra system.

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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    von zur Gathen, J. and Gerhard, J., Modern Computer Algebra, Cambridge Univ. Press, 2013, 3rd ed.CrossRefzbMATHGoogle Scholar
  2. 2.
    Bykov, V.I., Kytmanov, A.M., and Lazman, M.Z., Elimination Methods in Polynomial Computer Algebra, Kluwer, 1998.CrossRefzbMATHGoogle Scholar
  3. 3.
    Aizenberg, L.A., On one formula of the generalized multidimensional logarithmic residue and the solution of systems of nonlinear equations, Dokl. Akad. Nauk SSSR, 1977, vol. 234, no. 3, pp. 505–508.MathSciNetGoogle Scholar
  4. 4.
    Kytmanov, A.A., On analogues of the recurrent Newton formulas, Russ. Math., 2009, vol. 53, no. 10, pp. 34–44.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kytmanov, A.A., An algorithm for calculating power sums of roots for a class of systems of nonlinear equations, Program. Comput. Software, 2010, vol. 36, no. 2, pp. 103–110.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Kytmanov, A.A., Kytmanov, A.M., and Myshkina, E.K., Finding residue integrals for systems of non-algebraic equations in Cn, J. Symbol. Comput., 2015, vol. 66, pp. 98–110.CrossRefzbMATHGoogle Scholar
  7. 7.
    Kytmanov, A.M. and Naprienko, Y.M., An approach to define the resultant of two entire functions, J. Complex Var. Elliptic Equations, 2017, vol. 62, no. 2, pp. 269–286.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Whittaker, E.T. and Watson, G.N., A Course of Modern Analysis, Cambridge Univ. Press, 1927.zbMATHGoogle Scholar
  9. 9.
    Kuzovatov, V.I. and Kytmanov, A.M., On one analog of Plan’s formula, Izv. Nats. Akad. Nauk Arm., Mat., 2018, vol. 53, no. 3 (in press).Google Scholar
  10. 10.
    Kuzovatov, V.I., On one generalization of Plan’s formula, Izv. Vyssh. Uchebn. Zaved., Mat., 2018 (in press).Google Scholar
  11. 11.
    Kytmanov, A.M. and Myslivets, S.G., On the zetafunction of systems of nonlinear equations, Sib. Math. J, 2007, vol. 48, no. 5, pp. 863–870.CrossRefzbMATHGoogle Scholar
  12. 12.
    Titchmarsh, E.C., The Theory of the Riemann Zeta-Function, Oxford Univ. Press, 1951.zbMATHGoogle Scholar
  13. 13.
    Gel'fand, I.M. and Levitan, B.M., On one simple identity for eigenvalues of the second-order differential operator, Dokl. Akad. Nauk SSSR, 1953, vol. 88, no. 4, pp. 593–596.Google Scholar
  14. 14.
    Dikii, L.A., Zeta function of the ordinary differential equation on a finite segment, Izv. Akad. Nauk SSSR, Ser. Mat., 1955, vol. 19, no. 4, pp. 187–200.MathSciNetGoogle Scholar
  15. 15.
    Dikii, L.A., Formulas of traces for Sturm–Liouville differential operators, Usp. Mat. Nauk, 1958, vol. 13, no. 3, pp. 111–143.Google Scholar
  16. 16.
    Lidskii, V.B. and Sadovnichii, V.A., Regularized sums of zeros of a class of entire functions, Funct. Anal. Appl., 1967, vol. 1, no. 2, pp. 133–139.CrossRefzbMATHGoogle Scholar
  17. 17.
    Smagin, S.A. and Shubin, M.A., On the zeta-function of a transversally elliptic operator, Russ. Math. Surv., 1984, vol. 39, no. 2, pp. 201–202.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kuzovatov, V.I. and Kytmanov, A.A., On the zetafunction of zeros of some class of entire functions, J. Sib. Fed. Univ. Math. Phys., 2014, vol. 7, no. 4, pp. 489–499.CrossRefGoogle Scholar
  19. 19.
    Bieberbach, L., Analytische Fortsetzung, Springer, 1955.CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Siberian Federal UniversityKrasnoyarskRussia

Personalised recommendations

Cite article

Buy options