Geodesic
Trace formula for integral points on the three-dimensional sphere
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 13-15.

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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. 
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V. A. Bykovskii; M. D. Monina. Trace formula for integral points on the three-dimensional sphere. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 490 (2020), pp. 13-15. http://geodesic.mathdoc.fr/item/DANMA_2020_490_a2/

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