Yudin, V. A. Sphere-packing in Euclidean space and extremal problems for trigonometrical polynomials. (English. Russian original) Zbl 0777.52012 Discrete Math. Appl. 1, No. 1, 69-72 (1991); translation from Diskretn. Mat. 1, No. 2, 155-158 (1989). Summary: An upper bound for the number of disjoint spheres of radius \(\varepsilon\) in the \(n\)-dimensional torus \(T^ n\) is obtained by means of harmonic analysis. As a corollary, a new proof of Levenstein’s estimate for the density of packing of a metric space by spheres of equal radii is given. Cited in 4 Documents MSC: 52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry) Keywords:packing by spheres; \(n\)-dimensional torus; upper bound; density PDFBibTeX XMLCite \textit{V. A. Yudin}, Discrete Math. Appl. 1, No. 1, 69--72 (1989; Zbl 0777.52012); translation from Diskretn. Mat. 1, No. 2, 155--158 (1989) Full Text: DOI