Far Eastern Mathematical Journal

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On the distribution of integral points on the three-dimensional sphere


Monina M.D.

2020, issue 2, . 224226
DOI: https://doi.org/10.47910/FEMJ202022


Abstract
The result of V.A. Bykovsky and M.D. Monina on the distribution of integer points on the three-dimensional sphere $ a_1^2 + a_2^2 + a_3^2 + a_4^2 = d $ with odd $d$ is extended to the case of even $d$.

Keywords:
integral points on a sphere, modular functions, Hecke series

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References

[1] V. A. Bykovskii, M. D. Monina, Trace Formula for Integral Points on the Three-Dimensional Sphere, Doklady Mathematics, 101, (2020), 911 doi https://doi.org/10.1134/S1064562420010044.
[2] V. A. Bykovsky, Hecke series values of holomorphic cusp forms in the center of the critical strip, Number Theory in Progress. 2: Elementary and Analytic Number Theory, Walter de Gruyter, Berlin, 1999, 15 pp.
[3] Kh. Ivanets, E. Koval'skii, Analiticheskaia teoriia chisel, MTsNMO, M., 2014, 712 s.

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