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.
Similar content being viewed by others
References
von zur Gathen, J. and Gerhard, J., Modern Computer Algebra, Cambridge Univ. Press, 2013, 3rd ed.
Bykov, V.I., Kytmanov, A.M., and Lazman, M.Z., Elimination Methods in Polynomial Computer Algebra, Kluwer, 1998.
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.
Kytmanov, A.A., On analogues of the recurrent Newton formulas, Russ. Math., 2009, vol. 53, no. 10, pp. 34–44.
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.
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.
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.
Whittaker, E.T. and Watson, G.N., A Course of Modern Analysis, Cambridge Univ. Press, 1927.
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).
Kuzovatov, V.I., On one generalization of Plan’s formula, Izv. Vyssh. Uchebn. Zaved., Mat., 2018 (in press).
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.
Titchmarsh, E.C., The Theory of the Riemann Zeta-Function, Oxford Univ. Press, 1951.
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.
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.
Dikii, L.A., Formulas of traces for Sturm–Liouville differential operators, Usp. Mat. Nauk, 1958, vol. 13, no. 3, pp. 111–143.
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.
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.
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.
Bieberbach, L., Analytische Fortsetzung, Springer, 1955.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.I. Kuzovatov, A.A. Kytmanov, 2018, published in Programmirovanie, 2018, Vol. 44, No. 2.
Rights and permissions
About this article
Cite this article
Kuzovatov, V.I., Kytmanov, A.A. Algorithm for Constructing an Analog of Plan’s Formula. Program Comput Soft 44, 100–104 (2018). https://doi.org/10.1134/S036176881802007X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S036176881802007X