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On rational de Rham cohomology associated with the generalised confluent hypergeometric functions I, ℙ1 case

Published online by Cambridge University Press:  14 November 2011

Hironobu Kimura
Hironobu Kimura
Affiliation:
Department of Mathematics, Kumamoto University, Kumamoto 860, Japan
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Abstract

We define the rational de Rham cohomology associated with the generalised confluent hypergeometric functions. Purity of the cohomology is proved and an explicit ℂ-basis of the nontrivial cohomology is computed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 1 , 1997 , pp. 145 - 155
Copyright
Copyright © Royal Society of Edinburgh 1997

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References

1Aomoto, K.. Les équation aux différences linéaires et les intégrates des functions multiformes. J. Fac. Sci. Univ. Tokyo, Sect. IA Math. 22 (1975), 271–97.Google Scholar
2Gelfand, I. M.. General theory of hypergeometric functions. Dokl. Akad. Nauk. SSSR 288 (1986), 15–18; English translation: Soviet Math. Dokl. 33 (1986), 9–13.Google Scholar
3Gelfand, I. M., Retakh, V. S. and Serganova, V. V.. Generalized Airy functions, Schubert cells and Jordan groups. Dokl. Akad. Nauk. SSSR 298 (1988), 17–21; English translation: Soviet Math. Dokl. 37 (1988), 8–12.Google Scholar
4Haraoka, Y. and Kimura, H.. Contiguity relations of the generalised confluent hypergeometric functions. Proc. Japan Acad. 69 (1993), 105–10.Google Scholar
5Iwasaki, K., Kimura, H., Shimomura, S. and Yoshida, M.. From Gauss to Painlevé (Wiesbaden: Vieweg, 1991).CrossRefGoogle Scholar
6Kimura, H.. On Wronskian determination of confluent hypergeometric functions (Preprint, 1994).Google Scholar
7Kimura, H. and Koitabashi, T.. Normalizer of maximal abelian subgroups of GL(n) and general hypergeometric functions. Kumamoto J. Math. 9 (1996), 13–43.Google Scholar
8Kimura, H., Haraoka, Y. and Takano, K.. The generalised confluent hypergeometric functions. Proc. Japan Acad. Ser. A Math. Sci. 68 (1992), 290–5.CrossRefGoogle Scholar
9Kimura, H., Haraoka, Y. and Takano, K.. On confluence of the general hypergeometric systems. Proc. Japan Acad. Ser. A Math. Sci. 69 (1993), 99–104.CrossRefGoogle Scholar
10Kimura, H., Haraoka, Y. and Takano, K.. On contiguity relations of the confluent hypergeometric systems. Proc. Japan Acad. Ser. A Math. Sci. 70 (1994), 47–9.CrossRefGoogle Scholar
11Yoshida, M.. Fuchsian differential equations (Wiesbaden: Vieweg, 1987).CrossRefGoogle Scholar