Counting Lattice Points and O-Minimal Structures
- 10 June 2013
- journal article
- research article
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2014 (18) , 4932-4957
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 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.Keywords
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