论文标题
在一类超几何对角线上
On a Class of Hypergeometric Diagonals
论文作者
论文摘要
We prove that the diagonal of any finite product of algebraic functions of the form \begin{align*} {(1-x_1-\dots-x_n)^R}, \qquad R\in\mathbb{Q}, \end{align*} is a generalized hypergeometric function, and we provide an explicit description of its parameters.在[AKM2020，§3.2]中的Abdelaziz，Koutschan和Maillard的主要身份对应于Abdelaziz，Koutschan和Maillard的主要身份。我们的结果在这两个方向上都是有用的：一方面，它表明Christol的猜想对于大型的高几幅功能而言是正确的，另一方面，它允许对上述类型的代数功能的对角线具有非常明确的一般性观点。最后，与[AKM2020]相比，我们的证明是完全基本的，不需要任何算法帮助。
We prove that the diagonal of any finite product of algebraic functions of the form \begin{align*} {(1-x_1-\dots-x_n)^R}, \qquad R\in\mathbb{Q}, \end{align*} is a generalized hypergeometric function, and we provide an explicit description of its parameters. The particular case $(1-x-y)^R/(1-x-y-z)$ corresponds to the main identity of Abdelaziz, Koutschan and Maillard in [AKM2020, §3.2]. Our result is useful in both directions: on the one hand it shows that Christol's conjecture holds true for a large class of hypergeometric functions, on the other hand it allows for a very explicit and general viewpoint on the diagonals of algebraic functions of the type above. Finally, in contrast to [AKM2020], our proof is completely elementary and does not require any algorithmic help.
