$D$-finite multivariate series with arithmetic restrictions on their coefficients
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911366430851072 |
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| author | Bell, Jason Smertnig, Daniel |
| author_facet | Bell, Jason Smertnig, Daniel |
| contents | A multivariate, formal power series over a field $K$ is a Bézivin series if all of its coefficients can be expressed as a sum of at most $r$ elements from a finitely generated subgroup $G \le K^*$; it is a Pólya series if one can take $r=1$. We give explicit structural descriptions of $D$-finite Bézivin series and $D$-finite Pólya series over fields of characteristic $0$, thus extending classical results of Pólya and Bézivin to the multivariate setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_00415 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $D$-finite multivariate series with arithmetic restrictions on their coefficients Bell, Jason Smertnig, Daniel Combinatorics A multivariate, formal power series over a field $K$ is a Bézivin series if all of its coefficients can be expressed as a sum of at most $r$ elements from a finitely generated subgroup $G \le K^*$; it is a Pólya series if one can take $r=1$. We give explicit structural descriptions of $D$-finite Bézivin series and $D$-finite Pólya series over fields of characteristic $0$, thus extending classical results of Pólya and Bézivin to the multivariate setting. |
| title | $D$-finite multivariate series with arithmetic restrictions on their coefficients |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2202.00415 |