Geodesic
About one functional equation
Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 359-364 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\beta$, which sets an analytical continuation on the entire complex plane, except for the point $\alpha=1$, 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 $\beta$.
Keywords: Riemann zeta function, Dirichlet series, Hurwitz zeta function. 
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M. N. Dobrovol'skii; N. N. Dobrovol'skii; N. M. Dobrovol'skii. About one functional equation. Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 359-364. http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a26/

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[6] 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