论文标题
$ d $ - 最佳的多元系列系列具有算术限制的系数
$D$-finite multivariate series with arithmetic restrictions on their coefficients
论文作者
论文摘要
如果可以从有限生成的子组$ g \ le k^*$中将其所有系数表示为最多的$ r $元素，则在字段$ k $上进行的多元正式功率系列是Bézivin系列。如果可以服用$ r = 1 $，这是Pólya系列。我们在特征$ 0 $的字段上提供了$ d $ finitebézivin系列的$ d $ finitebézivin系列的明确结构描述，从而将Pólya和Bézivin的经典结果扩展到了多元环境。
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.
