JournalsrmiVol. 28, No. 3pp. 723–758

Nilsson solutions for irregular <var>A</var>-hypergeometric systems

  • Alicia Dickenstein

    Universidad de Buenos Aires, Argentina
  • Federico N. Martínez

    Universidad de Buenos Aires, Argentina
  • Laura Felicia Matusevich

    Texas A&M University, College Station, USA
Nilsson solutions for irregular <var>A</var>-hypergeometric systems cover
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Abstract

We study the solutions of irregular A-hypergeometric systems that are constructed from Gröbner degenerations with respect to generic positive weight vectors. These are formal logarithmic Puiseux series that belong to explicitly described Nilsson rings, and are therefore called (formal) Nilsson series. When the weight vector is a perturbation of (1, … ,1), these series converge and provide a basis for the (multivalued) holomorphic hypergeometric functions in a specific open subset of Cn\mathbb{C}^n. Our results are more explicit when the parameters are generic or when the solutions studied are logarithm-free. We also give an alternative proof of a result of Schulze and Walther that inhomogeneous A-hypergeometric systems have irregular singularities.

Cite this article

Alicia Dickenstein, Federico N. Martínez, Laura Felicia Matusevich, Nilsson solutions for irregular <var>A</var>-hypergeometric systems. Rev. Mat. Iberoam. 28 (2012), no. 3, pp. 723–758

DOI 10.4171/RMI/689