About one functional equation
https://doi.org/10.22405/2226-8383-2021-22-5-359-364
Abstract
The hyperbolic zeta function of a two-dimensional lattice of Dirichlet approximations is studied. A functional equation is found for the hyperbolic zeta function of a two-dimensional
lattice of Dirichlet approximations in the case of rational 𝛽, which sets an analytical continuation on the entire complex plane, except for the point 𝛼 = 1, in which the pole is of the first order.
The found functional equation allows us to raise the question of continuity for the hyperbolic zeta function of a two-dimensional lattice of Dirichlet approximations in the case of rational 𝛽.
About the Authors
Михаил Добровольский
Геофизический центр РАН
Russian Federation
Russian Federation
Dobrovol’skii Mikhail Nikolaevich — candidate of candidate of physical and mathematical
sciences, Geophysical centre of RAS (Moscow).
e-mail: m.dobrovolsky@gcras.ru
Nikolai Nikolaevich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University; Tula State University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences, associate
professor
Nikolai Mikhailovich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
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8. Dobrovol’skaya, L. P., Dobrovol’skii, M. N., Dobrovol’skii, N. M. & Dobrovol’skii, N. N. 2014, “On Hyperbolic Zeta Function of Lattices”, Continuous and Distributed Systems. Solid Mechanics and Its Applications, vol. 211, pp. 23–62. doi: 10.1007/978-3-319-03146-0_2.
Review
For citations:
, Dobrovol’skii N.N., Dobrovol’skii N.M. About one functional equation. Chebyshevskii Sbornik. 2021;22(5):359-364. (In Russ.) https://doi.org/10.22405/2226-8383-2021-22-5-359-364
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