Exceptional sets of hypergeometric series

Journal of Number Theory

Volumn 101, Issue 2, 2003, Pages 244-269

  Archinard, Natália ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Algebraic evaluations; Hypergeometric abelian varieties; Identities

Indexed keywords

EID: 0042706477     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-314X(03)00042-8     Document Type: Article

References (31)

1. M. Abramowitz, I.A. Stegun (Eds.), Handbook of Mathematical Functions, National Bureau of Standards, USA, 1964.
2. Y. André, G-fonctions et transcendance, J. Reine Angew. Math. 476 (1996) 95-125.
3. N. Archinard, Hypergeometric abelian varieties, Can. J. Math., to appear.
4. N. Archinard, Abelian varieties and identities for hypergeometric series, Ph.D. Thesis, ETH Zürich, 2000, http://e-collection.ethbib.ethz.ch.
5. F. Beukers, Algebraic values of G-functions, J. Reine Angew. Math. 434 (1993) 45-65.
6. F. Beukers, J. Wolfart, Algebraic values of hypergeometric functions, in: A. Baker (Ed.), New Advances in Transcendence Theory, Cambridge University Press, Cambridge, 1986.
7. P.B. Cohen, Perspectives de l'approximation diophantienne et de la transcendance, Ramanujan Journal, to appear.
8. P. Cohen, J. Wolfart, Modular embeddings for some non-arithmetic Fuchsian groups, Acta Arith. 56 (1990) 93-110.
9. P.B. Cohen, J. Wolfart, Fonctions hypergéométriques en plusieurs variables et espaces des modules de variétés abéliennes, Ann. Scient. Éc. Norm. Sup. (4) 26 (1993) 665-690.
10. P.B. Cohen, G. Wüstholz, Applications of the André-Oort Conjecture to transcendence, in: G. Wüstholz (Ed.), A Panorama in Number Theory, Cambridge University Press, Cambridge, 2001.
11. P.-A. Desrousseaux, Valeurs exceptionelles de fonctions hypergéométriques d'Appell, Ramanujan Journal, submitted for publication.
12. S. Edixhoven, A. Yafaev, Subvarieties of Shimura varieties, Ann. Math., to appear.
13. M. Flach, Periods and special values of the hypergeometric series, Math. Proc. Camb. Phil. Soc. 106 (1989) 389-401.
14. H. Gross (with an appendix by D. Rohrlich), On the periods of abelian integrals and a formula of Chowla and Selberg, Invent. Math. 45 (1978) 193-211.
15. K. Iwasaki, H. Kimura, S. Shimomura, M. Yoshida, From Gauss to Painlevé, A Modern Theory of Special Functions, Aspects of Mathematics, Vieweg, Braunschweig, 1991.
16. G.S. Joyce, I.J. Zucker, Special values of the hypergeometric series, Math. Proc. Camb. Phil. Soc. 109 (1991) 257-261.
17. F. Klein (ausgearbeitet und vervollständigt von R. Fricke), Theorie der elliptischen Modulfunctionen, B.G. Teubner, Leipzig, 1890.
18. S. Lang, Elliptic Functions, Springer, Berlin, 1987.
19. Z. Nehari, Conformal Mapping, McGraw-Hill Book Company, Inc., New York, 1952.
20. H.A. Schwarz, Ueber diejenigen Fälle, in welchen die Gaussische hypergeometrische Reihe eine algebraische Function ihres vierten Elementes darstellt, J. Reine Angew. Math. 75 (1873) 292-335.
21. H. Shiga, J. Wolfart, Criteria for complex multiplication and transcendence properties of automorphic functions, J. Reine Angew. Math. 463 (1995) 1-25.
22. C.L. Siegel, Ueber einige Anwendungen diophantischer Approximationen, in: Ges. Werke, Bd 1, Springer, Berlin, Heidelberg, New York, 1966, pp. 209-266.
23. P.F. Stiller, Classical automorphic forms and hypergeometric functions, J. Number Theory 28 (1988) 219-232.
24. K. Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan 29 (1977) 91-106.
25. H. Weber, Lehrbuch der Algebra, Vieweg und Sohn, Braunschweig, 1908.
26. E.T. Whittaker, G.N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge, 1915.
27. J. Wolfart, Fonctions hypergéometriques, arguments exceptionels et groupes de monodromie, Publ. Math. Univ. P. et M. Curie, Problèmes Diophantiens 79 (1985-86) 1-24.
28. J. Wolfart, Werte hypergeometrischer Funktionen, Invent. Math. 92 (1988) 187-216.
29. J. Wolfart, G. Wüstholz, Der Ueberlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen, Math. Ann. 273 (1985) 1-15.
30. G. Wüstholz, Algebraische Punkte auf analytischen Untergruppen algebraischer Gruppen, Ann. Math. 129 (1989) 501-517.
31. M. Yoshida, Hypergeometric Functions, My Love, Aspects of Mathematics, Vieweg, Braunschweig, 1997.