Abstract
Let N d (m) be the number of points of the integer lattice that belong to a d-dimensional ball of radius m (in the l 1- and l 2-norms). The aim of the paper is to study the asymptotic behavior of N d (m) as d → ∞, m → ∞. It is shown that if d tends to infinity much faster than m, then the asymptotic is different from the asymptotic volume of a d-dimensional ball of radius m. Bibliography: 6 titles.
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