Theta invariants and Lattice-Point Counting in Normed $\mathbb{Z}$-Modules
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914002276188160 |
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| author | Hajli, Mounir |
| author_facet | Hajli, Mounir |
| contents | Euclidean lattices occupy a central position in number theory, the geometry of numbers, and modern cryptography. In the present article, the theory of Euclidean lattices is employed to investigate normed $\mathbb{Z}$-modules of finite rank. Specifically, let $\overline{E}$ be a normed $\mathbb Z$-module of finite rank. We establish several inequalities for the lattice-point counting function of $\overline{E}$, along with related results. Our arguments rely primarily on the analytic properties of the theta series associated with Euclidean lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17406 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Theta invariants and Lattice-Point Counting in Normed $\mathbb{Z}$-Modules Hajli, Mounir Number Theory Euclidean lattices occupy a central position in number theory, the geometry of numbers, and modern cryptography. In the present article, the theory of Euclidean lattices is employed to investigate normed $\mathbb{Z}$-modules of finite rank. Specifically, let $\overline{E}$ be a normed $\mathbb Z$-module of finite rank. We establish several inequalities for the lattice-point counting function of $\overline{E}$, along with related results. Our arguments rely primarily on the analytic properties of the theta series associated with Euclidean lattices. |
| title | Theta invariants and Lattice-Point Counting in Normed $\mathbb{Z}$-Modules |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.17406 |