#### Lectures in mathematics : Kyoto University

##### vol. 15

Lectures on algebraic solutions of hypergeometric differential equations / by Michihiko Matsuda

c1985

Chapter I. Schwarz' theorem. | |

§ 1. Kummer's table and Gauss' transformations | 1 |

§ 2. Reducibility and logarithmic singularity | 7 |

§ 3. Schwarz' table | 13 |

Chapter II. Landau's criterion. | |

§ 4. Eisenstein's theorem | 20 |

§ 5. Landau's first and second theorems | 25 |

§ 6. Rough estimation | 33 |

Note. Honda's theorem | 42 |

Chapter III. Klein's settling. | |

§ 7. Reduction through Kummer's equation | 48 |

§ 8. Explicit description of algebraic solutions | 57 |

Chapter IV. Landau-Errera's theorem. | |

§ 9. Errera's lemma | 66 |

§ 10. Two lemmata | 74 |

§ 11. Attainment of Schwarz' table | 78 |

Chapter V. Transcendental liouvillian solutions. | |

§ 12. Picard-Vessiot's theory | 92 |

§ 13. Liouville's lemma | 96 |

§ 14. Kuga's theorem | 101 |

Note. Bessel's equation | 106 |

Bibliography | 110 |