We estimate the L^p norms of the discrepancy between the volume and the number of integer points in rO− x, a dilated by a factor r and translated by a vector x of a convex body O in R^d with smooth boundary with strictly positive curvature, (int_Rint_{T^d}|sum_{kin Z^d} chi_{rO-x}(k)−r^d|O||^p dxdμ(r−R))^{1/p} , where μ is a Borel measure compactly supported on the positive real axis and R →+∞.
(2019). Lp Norms of the Lattice Point Discrepancy [journal article - articolo]. In JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. Retrieved from http://hdl.handle.net/10446/135246
Lp Norms of the Lattice Point Discrepancy
Gariboldi, Bianca;Gigante, Giacomo
2019-01-01
Abstract
We estimate the L^p norms of the discrepancy between the volume and the number of integer points in rO− x, a dilated by a factor r and translated by a vector x of a convex body O in R^d with smooth boundary with strictly positive curvature, (int_Rint_{T^d}|sum_{kin Z^d} chi_{rO-x}(k)−r^d|O||^p dxdμ(r−R))^{1/p} , where μ is a Borel measure compactly supported on the positive real axis and R →+∞.File allegato/i alla scheda:
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Descrizione: This is a post-peer-review, pre-copyedit version of an article published in Journal of Fourier Analysis and Applications . The final authenticated version is available online at: http://dx.doi.org/10.1007/s00041-019-09665-1
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