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

M. D. Monina

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

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 $d.$

Key words: integral points on a sphere, modular functions, Hecke series.

UDC: 511.334+511.335

MSC: 11F11

Received: 28.10.2020

DOI: 10.47910/FEMJ202022