Density of subsets of squarefree elements in certain Dedekind domains
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916062341103616 |
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| author | Shin, Eunju |
| author_facet | Shin, Eunju |
| contents | We consider polynomial rings over finite fields and rings of integers of imaginary quadratic fields $\mathbb{Q}(\sqrt{-D})$. In this paper, we formulate the density of squarefree elements divisible by all elements of $T$ but by none of $P$, where $T$ and $P$ are subsets of squarefree elements and $T$ is finite. We also define Mersenne irreducibles in order to estimate the density of squarefree elements divisible by none of $P$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30466 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Density of subsets of squarefree elements in certain Dedekind domains Shin, Eunju Number Theory We consider polynomial rings over finite fields and rings of integers of imaginary quadratic fields $\mathbb{Q}(\sqrt{-D})$. In this paper, we formulate the density of squarefree elements divisible by all elements of $T$ but by none of $P$, where $T$ and $P$ are subsets of squarefree elements and $T$ is finite. We also define Mersenne irreducibles in order to estimate the density of squarefree elements divisible by none of $P$. |
| title | Density of subsets of squarefree elements in certain Dedekind domains |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.30466 |