Expansions in completions of global function fields
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910409651388416 |
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| author | Wang, Chunlin |
| author_facet | Wang, Chunlin |
| contents | It is well known that any power series over a finite field represents a rational function if and only if its sequence of coefficients is ultimately periodic. The famous Christol's Theorem states that a power series over a finite field is algebraic if and only if its sequence of coefficients is $p$-automatic. In this paper, we extend these two results to expansions of elements in the completion of a global function field under a nontrivial valuation. As application of our generalization of Christol's theorem, we answer some questions about $β$-expansions of formal Laurent series over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09175 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Expansions in completions of global function fields Wang, Chunlin Number Theory 11B85 It is well known that any power series over a finite field represents a rational function if and only if its sequence of coefficients is ultimately periodic. The famous Christol's Theorem states that a power series over a finite field is algebraic if and only if its sequence of coefficients is $p$-automatic. In this paper, we extend these two results to expansions of elements in the completion of a global function field under a nontrivial valuation. As application of our generalization of Christol's theorem, we answer some questions about $β$-expansions of formal Laurent series over finite fields. |
| title | Expansions in completions of global function fields |
| topic | Number Theory 11B85 |
| url | https://arxiv.org/abs/2404.09175 |