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EnglishLet Λ be a lattice in Graphic, and let Graphic be a definable family in an O-minimal structure over Graphic. We give sharp estimates for the number of lattice points in the fibers Graphic. Along the way, we show that for any subspace Graphic of dimension j>0 the j-volume of the orthogonal projection of ZT to Σ is, up to a constant depending only on the family Z, bounded by the maximal j-dimensional volume of the orthogonal projections to the j-dimensional coordinate subspaces.
http://hdl.handle.net/11384/13887| Titolo: | Counting lattice points and o-minimal structures |
| Autori interni: | BARROERO, Fabrizio |
| Data di pubblicazione: | 2014 |
| Rivista: | INTERNATIONAL MATHEMATICS RESEARCH NOTICES |
| Abstract: | Let Λ be a lattice in Graphic, and let Graphic be a definable family in an O-minimal structure over Graphic. We give sharp estimates for the number of lattice points in the fibers Graphic. Along the way, we show that for any subspace Graphic of dimension j>0 the j-volume of the orthogonal projection of ZT to Σ is, up to a constant depending only on the family Z, bounded by the maximal j-dimensional volume of the orthogonal projections to the j-dimensional coordinate subspaces. |
| Handle: | http://hdl.handle.net/11384/13887 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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