Geodesic
About one functional equation
Čebyševskij sbornik, Tome 22 (2021) no. 5, pp. 359-364

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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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     author = {M. N. Dobrovol'skii and N. N. Dobrovol'skii and N. M. Dobrovol'skii},
     title = {About one functional equation},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {359--364},
     publisher = {mathdoc},
     volume = {22},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2021_22_5_a26/}
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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/