Sharp o-minimality and lattice point counting

International Journal of Number Theory 2026 Open access

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Authors: Andrew Harrison-Migochi, Raymond McCulloch
DOI: 10.1142/s1793042126501046
Cited by: 0
References: 15

Abstract

Let [Formula: see text] be a lattice and let [Formula: see text] be a definable family in an o-minimal expansion of the real field, [Formula: see text]. A result of Barroero and Widmer gives sharp estimates for the number of lattice points in the fibers [Formula: see text]. Here we give an effective version of this result for a family definable in a sharply o-minimal structure expanding [Formula: see text]. We also give an effective version of the Barroero and Widmer statement for certain sets definable in [Formula: see text].

Fields of Study & Subjects

Advanced Algebra and Logic Advanced Topology and Set Theory Rough Sets and Fuzzy Logic

Publication details

Journal / source
International Journal of Number Theory
Publisher
World Scientific Pub Co Pte Ltd
Volume
22
Issue
09
Pages
1–19
Publication date
15 May 2026
Language
EN