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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.00415 |
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Table of 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.