---
res:
bibo_abstract:
- For d-dimensional ellipsoids E with dgreater than or equal to5 we show that the
number of lattice points in rE is approximated by the volume of rE, as r tends
to infinity, up to an error of order O(r(d-2)) for general ellipsoids and up to
an error of order o(r(d-2)) for irrational ones. The estimate refines earlier
bounds of the same order for dimensions dgreater than or equal to9. As an application
a conjecture of Davenport and Lewis about the shrinking of gaps between large
consecutive values of Q[m],mis an element ofZ(d) of positive definite irrational
quadratic forms Q of dimension dgreater than or equal to5 is proved. Finally,
we provide explicit bounds for errors in terms of certain Minkowski minima of
convex bodies related to these quadratic forms.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Friedrich
foaf_name: Götze, Friedrich
foaf_surname: Götze
foaf_workInfoHomepage: http://www.librecat.org/personId=10518
bibo_doi: 10.1007/s00222-004-0366-3
bibo_issue: '1'
bibo_volume: 157
dct_date: 2004^xs_gYear
dct_identifier:
- UT:000221850600006
dct_isPartOf:
- http://id.crossref.org/issn/0020-9910
dct_language: eng
dct_publisher: SPRINGER-VERLAG@
dct_title: Lattice point problems and values of quadratic forms@
...