We estimate the L p norms of the discrepancy between the volume and the number of integer points in r - x, a dilated by a factor r and translated by a vector x of a convex body in Rd with smooth boundary with strictly positive curvature,... R Td k. Zd.r - x ( k) - r d | | p dxd mu( r - R)... 1/ p, where mu is a Borel measure compactly supported on the positive real axis and R. +infinity
Colzani, L., Gariboldi, B., Gigante, G. (2019). L(p) Norms of the Lattice Point Discrepancy. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 25(4), 2150-2195 [10.1007/s00041-019-09665-1].
L(p) Norms of the Lattice Point Discrepancy
Colzani, L;Gariboldi, B;
2019
Abstract
We estimate the L p norms of the discrepancy between the volume and the number of integer points in r - x, a dilated by a factor r and translated by a vector x of a convex body in Rd with smooth boundary with strictly positive curvature,... R Td k. Zd.r - x ( k) - r d | | p dxd mu( r - R)... 1/ p, where mu is a Borel measure compactly supported on the positive real axis and R. +infinity
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