Algorithm for Constructing an Analog of Plan’s Formula
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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.
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References
- 1.von zur Gathen, J. and Gerhard, J., Modern Computer Algebra, Cambridge Univ. Press, 2013, 3rd ed.CrossRefMATHGoogle Scholar
- 2.Bykov, V.I., Kytmanov, A.M., and Lazman, M.Z., Elimination Methods in Polynomial Computer Algebra, Kluwer, 1998.CrossRefMATHGoogle Scholar
- 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.Kytmanov, A.A., On analogues of the recurrent Newton formulas, Russ. Math., 2009, vol. 53, no. 10, pp. 34–44.MathSciNetCrossRefMATHGoogle Scholar
- 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.MathSciNetCrossRefMATHGoogle Scholar
- 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.CrossRefMATHGoogle Scholar
- 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.MathSciNetCrossRefMATHGoogle Scholar
- 8.Whittaker, E.T. and Watson, G.N., A Course of Modern Analysis, Cambridge Univ. Press, 1927.MATHGoogle Scholar
- 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.Kuzovatov, V.I., On one generalization of Plan’s formula, Izv. Vyssh. Uchebn. Zaved., Mat., 2018 (in press).Google Scholar
- 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.CrossRefMATHGoogle Scholar
- 12.Titchmarsh, E.C., The Theory of the Riemann Zeta-Function, Oxford Univ. Press, 1951.MATHGoogle Scholar
- 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.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.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.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.CrossRefMATHGoogle Scholar
- 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.MathSciNetCrossRefMATHGoogle Scholar
- 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.Bieberbach, L., Analytische Fortsetzung, Springer, 1955.CrossRefMATHGoogle Scholar
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