Hyperbolic zeta function of two-dimensional diagonal unimodular lattices
https://doi.org/10.22405/2226-8383-2023-24-5-217-221
Abstract
The paper studies the properties of the hyperbolic zeta function of diagonal two-dimensional unimodular lattices. A theorem on the analytic continuation of this function is proved.
Keywords
hyperbolic zeta function of lattices,
metric lattice space,
unimodular lattices,
diagonal lattices,
fundamental lattices.
Supporting agencies: The study was carried out within the framework of state task No. 073-03-2022-117/7 on the topic “Numbertheoretic methods in approximate analysis and their applications in mechanics and physics” .
About the Authors
Alexander Petrovich Krylov
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
postgraduate student
Nikolai Mikhailovich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
1. Dobrovol’skaya, L. P., Dobrovol’skii, M. N., Dobrovol’skii, N. M. & Dobrovol’skii, N. N. 2012, “The hyperbolic Zeta function of grids and lattices, and calculation of optimal coefficients”, Chebyshevskii sbornik, vol. 13, no. 4(44), pp. 4-–107.
2. Kassels, D. 1965, Vvedenie v geometriyu chisel, [Introduction to the geometry of numbers], Mir, Moscow, (Russia).
3. Krylov, A. P., Dobrovolsky, N. M. 2022, “Metric space of two-dimensional diagonal unimodular lattices”, Notes of scientific seminars of the Tula School of Number Theory, Iss. 1, pp. 37–41.
4. 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.
Review
For citations:
Krylov A.P., Dobrovol’skii N.M. Hyperbolic zeta function of two-dimensional diagonal unimodular lattices. Chebyshevskii Sbornik. 2023;24(5):217-221. (In Russ.) https://doi.org/10.22405/2226-8383-2023-24-5-217-221
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