Geodesic
The Number of Lattice Points in a Spherical Layer
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 332-335 
V. A. Yudin. The Number of Lattice Points in a Spherical Layer. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 332-335. http://geodesic.mathdoc.fr/item/TM_2002_239_a22/
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     author = {V. A. Yudin},
     title = {The {Number} of {Lattice} {Points} in {a~Spherical} {Layer}},
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     url = {http://geodesic.mathdoc.fr/item/TM_2002_239_a22/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

New dependences between lattices and their duals are established. In Euclidean spaces of large dimensions, an exponential lower bound for the number of points of a lattice $L$ that lie in a spherical layer with close inner and outer radii is obtained. The radii are reciprocal to the packing radius of the dual lattice $L'$.

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