Let Λ be a lattice in, and let be a definable family in an O-minimal structure over. We give sharp estimates for the number of lattice points in the fibers. Along the way, we show that for any subspace of dimension j>0 the j-volume of the orthogonal projection of ZTto 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.
Barroero, F., Widmer, M. (2014). Counting lattice points and o-minimal structures. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2014(18), 4932-4957 [10.1093/imrn/rnt102].
Counting lattice points and o-minimal structures
Barroero F.;
2014-01-01
Abstract
Let Λ be a lattice in, and let be a definable family in an O-minimal structure over. We give sharp estimates for the number of lattice points in the fibers. Along the way, we show that for any subspace of dimension j>0 the j-volume of the orthogonal projection of ZTto 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.File in questo prodotto:
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