Continuity of Dirichlet series of 𝑠-dimensional lattices
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.
Supporting agencies: 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”
About the Authors
Roman Vladimirovich Tarabrin
Orenburg State University
Russian Federation
Russian Federation
postgraduate student
Nikolai Nikolaevich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Irina Yuryevna Rebrova
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
candidate of physical and mathematical sciences
Nikolai Mikhailovich Dobrovol’skii
Tula State Lev Tolstoy Pedagogical University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
References
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Review
For citations:
Tarabrin R.V., Dobrovol’skii N.N., Rebrova I.Yu., Dobrovol’skii N.M. Continuity of Dirichlet series of 𝑠-dimensional lattices. Chebyshevskii Sbornik. 2024;25(2):251-259. (In Russ.) https://doi.org/10.22405/2226-8383-2024-25-2-251-259
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