Journal of the Mathematical Society of Japan

The singular locus of Lauricella's $F_C$

Ryohei HATTORI and Nobuki TAKAYAMA

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We determine the singular locus of the holonomic system of differential equations annihilating Lauricella's hypergeometric function $F_C$ by the theory of $D$-modules and of Gröbner bases. We also study the $A$-hypergeometric system associated to $F_C$.

Article information

J. Math. Soc. Japan, Volume 66, Number 3 (2014), 981-995.

First available in Project Euclid: 24 July 2014

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Zentralblatt MATH identifier

Primary: 33C65: Appell, Horn and Lauricella functions
Secondary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials [See also 13Nxx, 32C38] 32C38: Sheaves of differential operators and their modules, D-modules [See also 14F10, 16S32, 35A27, 58J15]

Lauricella's hypergeometric differential equation singular locus $D$-module Gröbner basis $A$-hypergeometric systems


HATTORI, Ryohei; TAKAYAMA, Nobuki. The singular locus of Lauricella's $F_C$. J. Math. Soc. Japan 66 (2014), no. 3, 981--995. doi:10.2969/jmsj/06630981.

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