Monodromy for the hypergeometric function n F n ?1

Inventiones mathematicae - Tập 95 Số 2 - Trang 325-354 - 1989
Frits Beukers1, Gert Heckman2
1Department of Mathematics, University of Utrecht, Utrecht, The Netherlands
2Department of Mathematics, University of Leiden, Leiden, The Netherlands

Tóm tắt

Từ khóa


Tài liệu tham khảo

[Ba] Bailey, W.N.: On certain relations between hypergeometric series of higher order. J. London Math. Soc.8, 100?107 (1933)

[Bo] Borel, A.: Linear algebraic groups. New York: Benjamin 1969

[Bou] Bourbaki, N.: Groupes et Alg�bres de Lie, Chap. 4, 5, 6. Paris: Hermann 1981

[Co] Cohen, A.M.: Finite complex reflection groups. Ann. Sci. �c. Norm. Super., IU. Ser.9, 379?436 (1976); erratum in11, 613 (1978)

[E] Erd�lyi, A.: Higher transcendental functions, Vol I. Bateman Manuscript Project, New York: McGraw-Hill 1953

[Ho] Honda, T.: Algebraic differential equations. INDAM Symposia Math.XXIV, 169?204 (1981)

[Hu] Humphreys, J.E.: Introduction to Lie algebras and representation theory, Berlin-Heidelberg-New York: Springer 1972

[I] Ince, E.L.: Ordinary differential equations. Dover publ. 1956

[Kat] Katz, N.M.: Algebraic solutions of differential equations. Invent. Math.18, 1?118 (1972)

[Kap] Kaplansky, I.: An introduction to differential algebra. Paris: Hermann 1957

[Kl] Klein, F.: Vorlesungen �ber die hypergeometrische Funktion. Berlin-Heidelberg-New York: Springer 1933

[La] Landau, E.: Eine Anwendung des Eisensteinschen Satz auf die Theorie der Gausschen Differentialgleichung. J. Reine Angew. Math. 127 92?102 (1904); (reprinted in Collected Works, Vol. II, pp. 98?108, Thales Verlag, Esssen 1987

[Le] Levelt, A.H.M.: Hypergeometric functions. Thesis, University of Amsterdam 1961

[Mi] Mitchell, H.H.: Determination of all primitive collineation groups in more than four variables which contain homologies. Am. J. Math.36, 1?21 (1914)

[Mo] Mostow, G.D.: Braids, hypergeometric functions and lattices. Bull. Am. Math. Soc.16, 225?246 (1987)

[Pl] Plemelj, J.: Problems in the sense of Riemann and Klein. Interscience Publ. 1964

[Po] Pochhammer, L.: Zur Theorie der allgemeineren hypergeometrische Reihe. J. Reine Angew. Math. 102, 76?159 (1988)

[R] Riemann, B.: Gesammelte mathematische Werke, Teubner, Leipzig 1892

[Sc] Schwarz, H.A.: �ber diejenigen F�lle in welchen einer algebraische Funktion ihres vierten Elementes darstellt. Crelle J75, 292?335 (1873)

[ST] Shephard, G.C., Todd, J.A.: Finite unitary reflection groups. Can. J. Math.6, 274?304 (1954)

[T] Thomae, J.: �ber die h�heren hypergeometrischen Reihen. Math. Ann.2, 427?444 (1870)