Logarithmic A-hypergeometric series II
Logarithmic A-hypergeometric series II
复制标题
对数A-超几何级数II
DOI：
10.1007/s13366-022-00669-5
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
Go Okuyama and Mutsumi Saito
中科院分区：
文献类型：
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作者：
Masatoshi Takita;Yumi Izawa-Sugaya;佐伯恵里奈;Nakajima Sadahiko;Go Okuyama and Mutsumi Saito
在本文中，继（Saito in Int J Math 31（13）：2050 - 110，2020），我们继续发展构造正则A-超几何系统的对数级数解的扰动方法。在给定A-超几何系统的伪指数的情况下，考虑了一类常系数线性偏微分算子空间。比较这些空间，我们构造了一个基本的级数解系统与给定的指数的扰动方法。此外，我们给出了一个充分条件，一个给定的假指数是一个指数。作为主要结果的重要例子，我们分别给出了Aomoto-Gel'fand方程组和Lauricella方程组具有特殊参数向量的基本级数解系。
In this paper, following (Saito in Int J Math 31(13):2050110, 2020), we continue to develop the perturbing method of constructing logarithmic series solutions to a regularA-hypergeometric system. Fixing a fake exponent of anA-hypergeometric system, we consider some spaces of linear partial differential operators with constant coefficients. Comparing these spaces, we construct a fundamental system of series solutions with the given exponent by the perturbing method. In addition, we give a sufficient condition for a given fake exponent to be an exponent. As important examples of the main results, we give fundamental systems of series solutions to Aomoto-Gel’fand systems and to Lauricella’ssystems with special parameter vectors, respectively.