caa a22 4500 467989516 CHVBK 20180323112541.0 cr unu---uuuuu 170328e19900301xx s 000 0 eng 10.1007/BF01571276 doi (NATIONALLICENCE)springer-10.1007/BF01571276 Lattice points in high-dimensional spheres [Elektronische Daten] [J. Mazo, A. Odlyzko] LetN(x, n, α) denote the number of integer lattice points inside then-dimensional sphere of radius (an)1/2 with center at x. This numberN(x,n, α) is studied for α fixed,n → ∞, andx varying. The average value (asx varies) ofN(x,n, α) is just the volume of the sphere, which is roughly of the form (2 βe, α) n/2. it is shown that the maximal and minimal values ofN (x,n, α) differ from the everage by factors exponential inn, which is in contrast to the usual lattice point problems in bounded dimensions. This lattice point problem arose separately in universal quantization and in low density subset sum problems. Springer-Verlag, 1990 Mazo J. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA aut Odlyzko A. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA aut Monatshefte für Mathematik Springer-Verlag 110/1(1990-03-01), 47-61 0026-9255 110:1<47 1990 110 605 https://doi.org/10.1007/BF01571276 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01571276 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mazo J. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA aut NATIONALLICENCE 700 1- Odlyzko A. AT&T Bell Laboratories, 07974, Murray Hill, NJ, USA aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer-Verlag 110/1(1990-03-01), 47-61 0026-9255 110:1<47 1990 110 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer