<div class="csl-bib-body">
<div class="csl-entry">Freyer, A., & Henk, M. (2024). Polynomial bounds in Koldobsky’s discrete slicing problem. <i>Proceedings of the American Mathematical Society</i>, <i>152</i>(7), 3063–3074. https://doi.org/10.1090/proc/16753</div>
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dc.identifier.issn
0002-9939
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/209052
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dc.description.abstract
In 2013, Koldobsky posed the problem to find a constant dn, depending only on the dimension n, such that for any origin-symmetric convex body K ⊂ Rn there exists an (n - 1)-dimensional linear subspace H ⊂ Rn with |K ∩ Zn| ≤ dn |K ∩ H ∩ Zn| vol(K) n1 . In this article we show that dn is bounded from above by c n2 ω(n)/log(n), where c is an absolute constant and ω(n) is the flatness constant. Due to the recent best known upper bound on ω(n) we get a c n3 log(n)2 bound on dn. This improves on former bounds which were exponential in the dimension.
en
dc.language.iso
en
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dc.publisher
AMER MATHEMATICAL SOC
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dc.relation.ispartof
Proceedings of the American Mathematical Society
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dc.subject
lattice points
en
dc.subject
slicing problem
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dc.subject
bounds
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dc.title
Polynomial bounds in Koldobsky’s discrete slicing problem
