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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00705 |
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| _version_ | 1866916070604931072 |
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| author | Zou, Guixian |
| author_facet | Zou, Guixian |
| contents | Let $a$, $m$ be positive integers, $1<a<m$, $\gcd(a,m)=1$. We determine the location of a shortest vector in the $2$-dimensional lattices $$ Λ(a,m) = \{(x, y)\in\mathbb{Z}\times\mathbb{Z}\mid ax + y\equiv 0~(\bmod\,m)\}. $$ This confirms a conjecture of Han Wu and Guangwu Xu. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00705 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Locating a shortest vector in certain $2$-dimensional lattices Zou, Guixian Number Theory 11H06, 11H55, 11Y16 Let $a$, $m$ be positive integers, $1<a<m$, $\gcd(a,m)=1$. We determine the location of a shortest vector in the $2$-dimensional lattices $$ Λ(a,m) = \{(x, y)\in\mathbb{Z}\times\mathbb{Z}\mid ax + y\equiv 0~(\bmod\,m)\}. $$ This confirms a conjecture of Han Wu and Guangwu Xu. |
| title | Locating a shortest vector in certain $2$-dimensional lattices |
| topic | Number Theory 11H06, 11H55, 11Y16 |
| url | https://arxiv.org/abs/2606.00705 |