Geodesic
Continuity of Dirichlet series of $s$-dimensional lattices
Čebyševskij sbornik, Tome 25 (2024) no. 2, pp. 251-259.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this work, Dirichlet series of $s$-dimensional lattices are studied. In particular, the theorem is proved that the Dirichlet series of $s$-dimensional lattices are continuous on the space of lattices in the region of their absolute convergence. In conclusion, current problems for Dirichlet series of $s$-dimensional lattices that require further research are considered.
Keywords: Riemann zeta function, Dirichlet series, hyperbolic lattice zeta function. 
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Р. V. Tarabrin; N. N. Dobrovol'skii; I. Yu. Rebrova; N. M. Dobrovol'skii. Continuity of Dirichlet series of $s$-dimensional lattices. Čebyševskij sbornik, Tome 25 (2024) no. 2, pp. 251-259. http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a15/

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[2] Dobrovol'skii, N. M., Roshhenya, A. L., “On the number of lattice points in a hyperbolic cross”, Matematicheskie zametki, 63:4 (1998), 363–369 | DOI | MR | Zbl

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