A uniform formula on the number of integer matrices with given determinant and height

2024/07/11 by Muhammad Afifurrahman, Afifurrahman, Muhammad · 2 citations
Engineering · Mathematics · #11C20 (primary) #11D45 #11D72 #15B36 #Advanced Combinatorial Mathematics #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2407.08191

openalex publication_date 2024/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain an asymptotic formula for the number of integer 2× 2 matrices that have determinant Δ and whose absolute values of the entries are at most H. The result holds uniformly for a large range of Δ with respect to H.

Cited by

• Counting 2 × 2 integer matrices with a given determinant
• Distribution of integer points on determinant surfaces and a mod-p analogue

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