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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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/

[1] Jacobi C.G.J., Gesammelte werke, B., 1881

[2] Dirikhle P.L., Lektsii po teorii chisel, ONTI, M.–L., 1936

[3] Suetin P.K., Klassicheskie ortogonalnye mnogochleny, Fizmatlit, M., 2005

[4] Bykovsky V.A., “Hecke Series Values of Holomorphic Cusp Forms in the Centre of the Critical Strip”, Number Theory in Progress, v. 2, Elementary and Analytic Number Theory, eds. K. Gyory, H. Iwaniec, J. Urbanowicz, Walter de Gruyter, B., 1999, 675–689 | MR

[5] Delin P., Uspekhi matem. nauk, 30:5 (1975), 159–190 | MR

[6] Bykovskii V.A., Frolenkov D.A., “O vtorom momente L-ryadov golomorfnykh parabolicheskikh form na kriticheskoi pryamoi”, Izvestiya RAN. Seriya matematicheskaya, 2017, no. 2, 5–34 | DOI | Zbl