Counting basis extensions in a lattice

DOI10.1090/proc/16011zbMath1501.11069arXiv2011.05307OpenAlexW4214861744MaRDI QIDQ5097308

Maxwell Forst, Lenny Fukshansky

Publication date: 23 August 2022

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.05307

zbMATH Keywords

basisinteger latticeFarey fractionsmultilinear formprimitive vectorscounting lattice pointsextending to a basis

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Polynomials in number theory (11C08) Lattices and convex bodies (number-theoretic aspects) (11H06) Representation problems (11D85) Matrices, determinants in number theory (11C20)

Related Items (1)

On lattice extensions

Cites Work

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• Natural density of rectangular unimodular integer matrices
• Diophantine approximation with square-free numbers
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• On the completion of a partial integral matrix to a unimodular matrix
• Representing integers by multilinear polynomials
• Integral points of small height outside of a hypersurface
• On the probability that \(k\) positive integers are relatively prime
• An introduction to the geometry of numbers.
• A Sharp Bound for Solutions of Linear Diophantine Equations
• Lattice point counting and height bounds over number fields and quaternion algebras
• Natural density of integral matrices that can be extended to invertible integral matrices

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