Title | **Dimensions of solution spaces of H-systems** |

Author(s) | S.A. Abramov, M. Petkovšek |

Type | Article in Journal |

Abstract | An H -system is a system of first-order linear homogeneous recurrence equations for a single unknown function T , with coefficients which are polynomials with complex coefficients. We consider solutions of H -systems which are of the form T : dom ( T ) → C where either dom ( T ) = Z^d , or dom ( T ) = Z^d ∖ S and S is the set of integer singularities of the system. It is shown that any natural number is the dimension of the solution space of some consistent H -system, and that in the case d ≥ 2 there are H -systems whose solution space is infinite dimensional. The relationship between dimensions of solution spaces in the two cases dom ( T ) = Z^d and dom ( T ) = Z^d ∖ S is investigated. We prove that every consistent H -system H has a non-zero solution T with dom ( T ) = Z^d . Finally we give an appropriate corollary to the Ore–Sato theorem on possible forms of solutions of H -systems in this setting. |

Keywords | Hypergeometric systems, Existence of non-zero solutions, Dimensions of solution spaces, Ore–Sato theorem |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S074771710700154X |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 43 |

Number | 5 |

Pages | 377 - 394 |

Year | 2008 |

Edition | 0 |

Translation |
No |

Refereed |
No |