Sizes of Pre-Images of the Minimal Euclidean Function on the Gaussian Integers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917339166932992 |
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| author | Graves, Hester |
| author_facet | Graves, Hester |
| contents | In 2023, the author presented the first computable minimal Euclidean function for a non-trivial number field. Along with a formula for $ϕ_{\mathbb{Z}[i]}$, the minimal Euclidean function on the Gaussian inteers, the same paper introduced a geometric description for $ϕ_{\mathbb{Z}[i]}^{-1}([0,n])$. This paper uses that construction to prove formulas for the size of the function's pre-images, or $|ϕ_{\mathbb{Z}[i]}^{-1}([0,n])|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_13225 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sizes of Pre-Images of the Minimal Euclidean Function on the Gaussian Integers Graves, Hester Number Theory 11R11, 11R04, 11A05 In 2023, the author presented the first computable minimal Euclidean function for a non-trivial number field. Along with a formula for $ϕ_{\mathbb{Z}[i]}$, the minimal Euclidean function on the Gaussian inteers, the same paper introduced a geometric description for $ϕ_{\mathbb{Z}[i]}^{-1}([0,n])$. This paper uses that construction to prove formulas for the size of the function's pre-images, or $|ϕ_{\mathbb{Z}[i]}^{-1}([0,n])|$. |
| title | Sizes of Pre-Images of the Minimal Euclidean Function on the Gaussian Integers |
| topic | Number Theory 11R11, 11R04, 11A05 |
| url | https://arxiv.org/abs/2603.13225 |