Nilsson solutions for irregular A-hypergeometric systems

DOI10.4171/RMI/689zbMath1251.33012arXiv1007.4225MaRDI QIDQ446408

Federico N. Martínez, Laura Felicia Matusevich, Alicia Dickenstein

Publication date: 6 September 2012

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.4225

zbMATH Keywords

\(A\)-hypergeometric functionsformal Nilsson seriesGröbner degenerations in the Weyl algebrairregular holonomic \(D\)-modules

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Other hypergeometric functions and integrals in several variables (33C70) Sheaves of differential operators and their modules, (D)-modules (32C38) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10)

Related Items (6)

Torus equivariant \(D\)-modules and hypergeometric systems ⋮ On the parametric behavior of $A$-hypergeometric series ⋮ Logarithmic A-hypergeometric series ⋮ Gevrey and formal Nilsson solutions of \(A\)-hypergeometric systems ⋮ On the local monodromy of \(A\)-hypergeometric functions and some monodromy invariant subspaces ⋮ Irregular modified $A$-hypergeometric systems

Cites Work

• Irregular hypergeometric \(\mathcal D\)-modules
• Hypergeometric functions and rings generated by monomials
• The Gröbner fan of an \(A_n\)-module
• Hypergeometric functions and toric varieties
• The Structure of Bivariate Rational Hypergeometric Functions
• Gevrey solutions of the irregular hypergeometric system associated with an affine monomial curve
• Singularities of the hypergeometric system associated with a monomial curve
• Formal Solutions of Irregular Linear Differential Equations. Part I
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