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Chebyshevskii Sbornik, 2024, Volume 25, Issue 2, Pages 251–259
DOI: https://doi.org/10.22405/2226-8383-2024-25-2-251-259 (Mi cheb1430) 		 
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Continuity of Dirichlet series of $s$-dimensional lattices

Р. V. Tarabrina, N. N. Dobrovol'skiib, I. Yu. Rebrovab, N. M. Dobrovol'skiib

a Orenburg State University (Orenburg)
b Tula State Lev Tolstoy Pedagogical University (Tula)
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DOI: https://doi.org/10.22405/2226-8383-2024-25-2-251-259
Abstract: 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.
Funding agency Grant number
Russian Science Foundation 23-21-00317
The work has been prepared by the RSF grant № 23-21-00317 “Geometry of numbers and Diophantine approximations in the number-theoretic method in approximate analysis”.
Received: 12.04.2024
Accepted: 28.06.2024
Document Type: Article
UDC: 511.3
Language: Russian
Citation: Р. V. Tarabrin, N. N. Dobrovol'skii, I. Yu. Rebrova, N. M. Dobrovol'skii, “Continuity of Dirichlet series of $s$-dimensional lattices”, Chebyshevskii Sb., 25:2 (2024), 251–259
Citation in format AMSBIB
\Bibitem{TarDobReb24}
\by Р.~V.~Tarabrin, N.~N.~Dobrovol'skii, I.~Yu.~Rebrova, N.~M.~Dobrovol'skii
\paper Continuity of Dirichlet series of $s$-dimensional lattices
\jour Chebyshevskii Sb.
\yr 2024
\vol 25
\issue 2
\pages 251--259
\mathnet{http://mi.mathnet.ru/cheb1430}
\crossref{https://doi.org/10.22405/2226-8383-2024-25-2-251-259}
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