Geodesic
Hyperbolic zeta function of two-dimensional diagonal unimodular lattices
Čebyševskij sbornik, Tome 24 (2023) no. 5, pp. 217-221.

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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. 
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A. P. Krylov; N. M. Dobrovolsky. Hyperbolic zeta function of two-dimensional diagonal unimodular lattices. Čebyševskij sbornik, Tome 24 (2023) no. 5, pp. 217-221. http://geodesic.mathdoc.fr/item/CHEB_2023_24_5_a14/

[1] Dobrovol'skaya, L. P., Dobrovol'skii, M. N., Dobrovol'skii, N. M., Dobrovol'skii, N. N., “The hyperbolic Zeta function of grids and lattices, and calculation of optimal coefficients”, Chebyshevskii sbornik, 13:4(44) (2012), 4–107 | Zbl

[2] Kassels, D., Introduction to the geometry of numbers, Mir, M., 1965 (Russia)

[3] Krylov, A. P., Dobrovolsky, N. M., “Metric space of two-dimensional diagonal unimodular lattices”, Notes of scientific seminars of the Tula School of Number Theory, 2022, no. 1, 37–41 | DOI

[4] Dobrovolskaya L. P., Dobrovolsky M. N., Dobrovol'skii N. M., Dobrovolsky N. N., “On Hyperbolic Zeta Function of Lattices”, Continuous and Distributed Systems. Solid Mechanics and Its Applications, 211 (2014), 23–62 | DOI | MR | Zbl