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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 490, Pages 13–15
DOI: https://doi.org/10.31857/S268695432001004X (Mi danma24) 		 
MATHEMATICS

Trace formula for integral points on the three-dimensional sphere

V. A. Bykovskii, M. D. Monina

Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Khabarovsk, Russian Federation
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DOI: https://doi.org/10.31857/S268695432001004X
Abstract: Average values over integral points on a three-dimensional sphere with an arbitrary smooth weight function are studied. For them, an expansion of the mean product of two L-series associated with the Hecke basis in spaces of holomorphic parabolic forms of integer even weight with respect to the congruence subgroup $\Gamma_0$(4) is obtained.
Keywords: integral points on a sphere, modular functions, L-series of parabolic forms.
Funding agency Grant number
Russian Science Foundation 19–11–00065
This work was supported by the Russian Science Foundation, project no. 19-11-00065.
Received: 24.10.2019
Revised: 24.10.2019
Accepted: 01.11.2019
English version:
Doklady Mathematics, 2020, Volume 101, Issue 1, Pages 9–11
DOI: https://doi.org/10.1134/S1064562420010044
Bibliographic databases:
Document Type: Article
UDC: 511.334+511.335
Language: Russian
Citation: V. A. Bykovskii, M. D. Monina, “Trace formula for integral points on the three-dimensional sphere”, Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020), 13–15; Dokl. Math., 101:1 (2020), 9–11
Citation in format AMSBIB
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\transl
\jour Dokl. Math.
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\pages 9--11
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