LATTICE POINTS IN MANY-DIMENSIONAL BALLS

摘要

Let P_k(n) be the difference between the number of points of the integer lattice contained in the ball y_1~2 + • • •+ y_k~2≤ n and the volume of this ball. The paper investigates the asymptotic behavior of the sums ∑_(n≤x) P_k(n) (k≥4), ∑_(n≤x) P_3~2(n), ∑_(n≤x) P_4~2(n) as x→+∞. Bibliography: 15 titles.