相关论文: The singular locus of Lauricella's F_C

We study the fundamental group of the complement of the singular locus of Lauricella's hypergeometric function $F_C$ of $n$ variables. The singular locus consists of $n$ hyperplanes and a hypersurface of degree $2^{n-1}$ in the complex…

In this paper, we give a set of generators and relations of the fundamental group of the non-singular locus of Lauricella's hypergeometric functions

We derive Groebner bases for Lauricella's hypergeometric differential equations $I_A(m), I_B(m), I_C(m)$ with respect to a monomial order. By using these Groebner bases, we determine characteristic varieties and the singular loci of…

We study the conditions under which the monodromy group for Lauricella's hypergeometric function $F_C (a,b,c;x)$ is finite irreducible. We give the conditions in terms of the parameters $a,b,c$. In addition, we discuss the structure of the…

We study the monodromy representation of the system $E_C$ of differential equations annihilating Lauricella's hypergeometric function $F_C$ of $m$ variables. Our representation space is the twisted homology group associated with an integral…

We study binomial D-modules, which generalize A-hypergeometric systems. We determine explicitly their singular loci and provide three characterizations of their holonomicity. The first of these states that a binomial D-module is holonomic…

We study the monodromy representation of the generalized hypergeometric differential equation and that of Lauricella's $F_C$ system of hypergeometric differential equations. We use fundamental systems of solutions expressed by the…

We give the monodromy representations of local systems of twisted homology groups associated with Lauricella's system $F_D(a,b,c)$ of hypergeometric differential equations under mild conditions on parameters. Our representation is effective…

Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the…

We define a hypergeometric series in $m$ variables with $p+(p-1)m$ parameters, which reduces to the generalized hypergeometric series $_pF_{p-1}$ when $m=1$, and to Lauricella's hypergeometric series $F_C$ in $m$ variables when $p=2$. We…

One-loop two-, three- and four-point scalar functions are analytically integrated directly such that they are expressed in terms of Lauricella's hypergeometric function $F_D$. For two- and three-point functions, exact expressions are…

We study Lauricella's hypergeometric function F_C by using twisted (co)homology groups. We construct twisted cycles with respect to an Euler-type integral representation of F_C. These cycles correspond to 2^m linearly independent solutions…

We present a further extension of the HYPERDIRE project, which is devoted to the creation of a set of Mathematica-based program packages for manipulations with Horn-type hypergeometric functions on the basis of differential equations.…

We give a new proof of the rearrangement lemma that works for all dimensions and all heat coefficients in the study of modular geometry on noncommutative tori. The building blocks of the spectral functions are landed in a hypergeometric…

This paper, pursuing the work started in [10] and [11], holds six new formulae for {\pi}, see equations, through ratios of first kind elliptic integrals and some values of hypergeometric functions of three or four variables of Lauricella…

Recently found all the fundamental solutions of a multidimensional singular elliptic equation are expressed in terms of the well-known Lauricella hypergeometric function in many variables. In this paper, we find a unique solution of the…

We study contiguity relations of Lauricella's hypergeometric function F_D, by using the twisted cohomology group and the intersection form. We derive contiguity relations from those in the twisted cohomology group and give the coefficients…

We prove finite field analogues of integral representations of Appell- Lauricella hypergeometric functions in many variables. We consider certain hypersurfaces having a group action and compute the numbers of rational points associated with…

Let $E_C$ be the hypergeometric system of differential equations satisfied by Lauricella's hypergeometric series $F_C$ of $m$ variables. We show that the monodromy representation of $E_C$ is irreducible under our assumption consisting of…

We study the linear Pfaffian systems satisfied by a certain class of hypergeometric functions, which includes Gau\ss's ${}_2 F_{1}$, Thomae's ${}_L F_{L-1}$ and Appell-Lauricella's $F_D$. In particular, we present a fundamental system of…