Counting lattice points in central simple algebras with a given characteristic polynomial

We extend the asymptotic formula for counting integral matrices with a given irreducible characteristic polynomial by Eskin, Mozes and Shah in 1996 to the case of counting elements in a maximal order of certain central simple algebra with a given irreducible characteristic polynomial.

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Publication Details

Journal
ArXiv.org
Published
2025-03-04
Primary Topic
Advanced Algebra and Logic
Type
article
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article

Counting lattice points in central simple algebras with a given characteristic polynomial

Junling Xie
ArXiv.org
Advanced Algebra and Logic
article

Counting lattice points in central simple algebras with a given characteristic polynomial

Junling Xie
article en

Abstract

We extend the asymptotic formula for counting integral matrices with a given irreducible characteristic polynomial by Eskin, Mozes and Shah in 1996 to the case of counting elements in a maximal order of certain central simple algebra with a given irreducible characteristic polynomial.

ArXiv.org
Openalex Percentile: Top 69%
Advanced Algebra and Logic
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Counting lattice points in central simple algebras with a given characteristic polynomial — Junling Xie · ArXiv.org (2025) | TGRS Research Map | TGRS