Hilbert's tenth problem for rings of holomorphic functions of bounded order
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914839347068928 |
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| author | Pasten, Hector |
| author_facet | Pasten, Hector |
| contents | One of the main open problems in the context of extensions of Hilbert's tenth problem (HTP) is the case of the ring of complex entire functions in one variable. Our main result provides a step towards an answer: For every $ρ\ge 0$, we give a negative solution to the analogue of HTP in the ring of complex entire functions in one variable of growth order at most $ρ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12791 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hilbert's tenth problem for rings of holomorphic functions of bounded order Pasten, Hector Complex Variables Logic Number Theory Primary: 03B25, Secondary: 30D15, 11U05 One of the main open problems in the context of extensions of Hilbert's tenth problem (HTP) is the case of the ring of complex entire functions in one variable. Our main result provides a step towards an answer: For every $ρ\ge 0$, we give a negative solution to the analogue of HTP in the ring of complex entire functions in one variable of growth order at most $ρ$. |
| title | Hilbert's tenth problem for rings of holomorphic functions of bounded order |
| topic | Complex Variables Logic Number Theory Primary: 03B25, Secondary: 30D15, 11U05 |
| url | https://arxiv.org/abs/2406.12791 |