Algebraic degree of series of reciprocal algebraic integers
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929727538724864 |
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| author | Laursen, Mathias Løkkegaard |
| author_facet | Laursen, Mathias Løkkegaard |
| contents | In this paper, I give sufficient conditions for any linear combination in $\mathbb{Q}$ of numbers $\sum_{n=1}^{\infty}\frac{b_{1,n}}{α_{1,n}}$, $\ldots$, $\sum_{n=1}^{\infty}\frac{b_{K,n}}{α_{K,n}}$ to have algebraic degree greater than an arbitrary fixed integer $D$ when the numbers $α_{i,n}$ are algebraic integers of sufficiently rapidly increasing modulus and the $b_{i,n}$ are positive integers that are not too large. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_11786 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Algebraic degree of series of reciprocal algebraic integers Laursen, Mathias Løkkegaard Number Theory 11J72 In this paper, I give sufficient conditions for any linear combination in $\mathbb{Q}$ of numbers $\sum_{n=1}^{\infty}\frac{b_{1,n}}{α_{1,n}}$, $\ldots$, $\sum_{n=1}^{\infty}\frac{b_{K,n}}{α_{K,n}}$ to have algebraic degree greater than an arbitrary fixed integer $D$ when the numbers $α_{i,n}$ are algebraic integers of sufficiently rapidly increasing modulus and the $b_{i,n}$ are positive integers that are not too large. |
| title | Algebraic degree of series of reciprocal algebraic integers |
| topic | Number Theory 11J72 |
| url | https://arxiv.org/abs/2203.11786 |