Continuity of Dirichlet series of $s$-dimensional lattices
Čebyševskij sbornik, Tome 25 (2024) no. 2, pp. 251-259
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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.
@article{CHEB_2024_25_2_a15,
author = {{\CYRR}. V. Tarabrin and N. N. Dobrovol'skii and I. Yu. Rebrova and N. M. Dobrovol'skii},
title = {Continuity of {Dirichlet} series of $s$-dimensional lattices},
journal = {\v{C}eby\v{s}evskij sbornik},
pages = {251--259},
publisher = {mathdoc},
volume = {25},
number = {2},
year = {2024},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a15/}
}
TY - JOUR AU - Р. V. Tarabrin AU - N. N. Dobrovol'skii AU - I. Yu. Rebrova AU - N. M. Dobrovol'skii TI - Continuity of Dirichlet series of $s$-dimensional lattices JO - Čebyševskij sbornik PY - 2024 SP - 251 EP - 259 VL - 25 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a15/ LA - ru ID - CHEB_2024_25_2_a15 ER -
%0 Journal Article %A Р. V. Tarabrin %A N. N. Dobrovol'skii %A I. Yu. Rebrova %A N. M. Dobrovol'skii %T Continuity of Dirichlet series of $s$-dimensional lattices %J Čebyševskij sbornik %D 2024 %P 251-259 %V 25 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/CHEB_2024_25_2_a15/ %G ru %F CHEB_2024_25_2_a15
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/