Lattice points in high-dimensional spheres
作者： J. E. Mazo , A. M. Odlyzko
DOI: 10.1007/BF01571276
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摘要: LetN(x, n, α) denote the number of integer lattice points inside then-dimensional sphere radius (an)1/2 with center at x. This numberN(x,n, is studied for α fixed,n → ∞, andx varying. The average value (asx varies) ofN(x,n, just volume sphere, which roughly form (2 βe, α) n/2. it shown that maximal and minimal values ofN (x,n, differ from everage by factors exponential inn, in contrast to usual point problems bounded dimensions. problem arose separately universal quantization low density subset sum problems.
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sci-hub.se 参考文章(14)
A. Yudin, On the number of integer points in the displaced circles Acta Arithmetica. ,vol. 14, pp. 141- 152 ,(1968) , 10.4064/AA-14-2-141-152
Emil Grosswald, Representations of Integers as Sums of Squares ,(1985)
F. Fricker, Einführung in die Gitterpunktlehre Birkhäuser Basel. ,(1982) , 10.1007/978-3-0348-7185-3
József Beck, On a lattice point problem of L. Moser II Combinatorica. ,vol. 8, pp. 159- 176 ,(1988) , 10.1007/BF02122797
Hugh L. Montgomery, Minimal theta functions Glasgow Mathematical Journal. ,vol. 30, pp. 75- 85 ,(1988) , 10.1017/S0017089500007047
K. Chandrasekharan, Raghavan Narasimhan, On lattice-points in a random sphere Bulletin of the American Mathematical Society. ,vol. 73, pp. 68- 71 ,(1967) , 10.1090/S0002-9904-1967-11644-6
E. T. Whittaker, G. N. Watson, A Course of Modern Analysis ,(1902)
Richard Ernest Bellman, A Brief Introduction to Theta Functions ,(1960)
A. M. Frieze, On the Lagarias-Odlyzko algorithm for the subset sum problem SIAM Journal on Computing. ,vol. 15, pp. 536- 539 ,(1986) , 10.1137/0215038
On universal quantization IEEE Transactions on Information Theory. ,vol. 31, pp. 344- 347 ,(1985) , 10.1109/TIT.1985.1057034