论文信息 - Distribution of Lattice Points over the Four-Dimensional Sphere

Distribution of Lattice Points over the Four-Dimensional Sphere

AbstractLet rl(n) be the number of representations of n by a sum of l squares of integers and let 0 < A < 1 be a constant. It is proved that if (n,2)=1, then $$\Sigma _{ - A \leqslant w/\sqrt n \leqslant A{\text{ }}} r_3 (n - w^2 ) = \mu _4 (A)r_4 (n) + O(n^{1487/2000} ),\mu _4 (A) >0$$ . Previously, the author obtained this asymptotics with a weaker error term O( $$(n^{{3 \mathord{\left/ {\vphantom {3 {4 + \varepsilon }}} \right. \kern-\nulldelimiterspace} {4 + \varepsilon }}} )$$ . Bibliography: 12 titles.

O. M. Fomenko

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