Counting Lattice Points in The Sphere
β Scribed by Tsang, K.-M.
- Book ID
- 121418334
- Publisher
- Oxford University Press
- Year
- 2000
- Tongue
- English
- Weight
- 182 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0024-6093
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π SIMILAR VOLUMES
The old problem of counting lattice points in euclidean spheres leads to use Jacobi theta functions and its relatives as generating functions. Important lattices (root systems, the Leech lattice) can be constructed from algebraic codes and analogies between codes and lattices have been extensively s
The number of visible (primitive) lattice points in the sphere of radius R is well approximated by 4Ο 3ΞΆ(3) R 3 . We consider an integral expression involving the error term E \* (R), which leads to ). This is comparable to what is known in the sphere problem. We can avoid the use of the second pow
P : (n) x n: , where A is the set of all vertices of P and each P : (n) is a certain periodic function of n. The Ehrhart reciprocity law follows automatically from the above formula. We also present a formula for the coefficients of Ehrhart polynomials in terms of elementary symmetric functions. 200