×

On the distribution of integral points on the three-dimensional sphere. (Russian. English summary) Zbl 1454.11102

Summary: The result of V. A. Bykovsky and the author [“Trace formula for integral points on the three-dimensional sphere”, Dokl. Math. 101, 9–11 (2020; doi:10.1134/S1064562420010044)] 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 \(d\).

MSC:

11F72 Spectral theory; trace formulas (e.g., that of Selberg)
11F11 Holomorphic modular forms of integral weight
PDFBibTeX XMLCite
Full Text: DOI MNR

References:

[1] V. A. Bykovskii, M. D. Monina, “Trace Formula for Integral Points on the Three-Dimensional Sphere”, Doklady Mathematics, 101 (2020), 9-11 · Zbl 1476.11130 · doi: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, v. 2, Elementary and Analytic Number Theory, eds. Ed. by K. Gyory, H. Iwaniec, and J. Urbanowicz, Walter de Gruyter, Berlin, 1999, 675-690 · Zbl 0983.11021
[3] Kh. Ivanets, E. Kovalskii, Analiticheskaya teoriya chisel, MTsNMO, M., 2014, 712 pp.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.