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. 
@article{DANMA_2020_490_a2,
     author = {V. A. Bykovskii and M. D. Monina},
     title = {Trace formula for integral points on the three-dimensional sphere},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {13--15},
     publisher = {mathdoc},
     volume = {490},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_490_a2/}
}
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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/