Lectures in mathematics : Kyoto University

vol. 15

Lectures on algebraic solutions of hypergeometric differential equations / by Michihiko Matsuda
c1985

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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

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