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.
Titolo: | Counting lattice points and o-minimal structures |
Autori: | |
Data di pubblicazione: | 2014 |
Rivista: | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1093/imrn/rnt102 |
Handle: | http://hdl.handle.net/11384/13887 |
Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.