On the transcendency of the values of the modular function at algebraic points
Journées arithmétiques de Genève - 9-13 septembre 1991, Astérisque, no. 209 (1992), pp. 293-305 
@incollection{AST_1992__209__293_0,
     author = {Shiga, Hironori},
     title = {On the transcendency of the values of the modular function at algebraic points},
     booktitle = {Journ\'ees arithm\'etiques de Gen\`eve - 9-13 septembre 1991},
     editor = {Coray D. F. and P\'etermann Y.-F. S},
     series = {Ast\'erisque},
     pages = {293--305},
     year = {1992},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {209},
     zbl = {0862.11046},
     language = {en},
     url = {https://www.numdam.org/item/AST_1992__209__293_0/}
}
TY  - CHAP
AU  - Shiga, Hironori
TI  - On the transcendency of the values of the modular function at algebraic points
BT  - Journées arithmétiques de Genève - 9-13 septembre 1991
AU  - Collectif
ED  - Coray D. F.
ED  - Pétermann Y.-F. S
T3  - Astérisque
PY  - 1992
SP  - 293
EP  - 305
IS  - 209
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_1992__209__293_0/
LA  - en
ID  - AST_1992__209__293_0
ER  - 
%0 Book Section
%A Shiga, Hironori
%T On the transcendency of the values of the modular function at algebraic points
%B Journées arithmétiques de Genève - 9-13 septembre 1991
%A Collectif
%E Coray D. F.
%E Pétermann Y.-F. S
%S Astérisque
%D 1992
%P 293-305
%N 209
%I Société mathématique de France
%U https://www.numdam.org/item/AST_1992__209__293_0/
%G en
%F AST_1992__209__293_0
Shiga, Hironori. On the transcendency of the values of the modular function at algebraic points, dans Journées arithmétiques de Genève - 9-13 septembre 1991, Astérisque, no. 209 (1992), pp. 293-305. https://www.numdam.org/item/AST_1992__209__293_0/

[B] Bertrand, D., Lemme de zéros et nombres transcendants, Seminaire Bour-baki, (1985-86). | EuDML | Numdam | Zbl

[B-W] Beukers, F., Wolfart, J., Algebraic values of hypergeometric functions, Proceedings of Durham conference on transcendental numbers 1986. | Zbl

[H-I] Hashimoto, K., Ibukiyama, T., On class numbers of positive definite binary quaternion hermitian forms, J. Fac. Sci. Univ. Tokyo 27 (1980), 549-601. | Zbl

[I] Igusa, J., On Siegel Modular forms of genus two, Amer. J. Math. 84 (1962), 175-200. | Zbl | DOI

[Mo] Morita, Y., On transcendency of special values of arithmetic automorphic functions, J. Math. Soc. Japan 24 (1972), 268-274. | Zbl | DOI

[Mu] Mumford, D., Tata lectures on thêta I. | Zbl

[S-T] Shimura, G., Taniyama, Y., Complex multiplication of abelian varieties and its applications to number theory, Math. Soc. Japan (1975).

[S] Shiga, H., On the representation of the Picard modular function by theta constants I-II, Pub. Research Inst. Kyoto Univ. 24 (1988), 311-360. | Zbl

[T] Takeuchi, K., A characterization of arithmetic Fuchsian groups, J. Math. Soc. Japan 27 (1975), 600-612. | Zbl | DOI

[W-W] Wolfart, J., Wüstholz, G., Der Überlangerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen, Math. Ann. 273 (1985), 1-15. | Zbl | EuDML | DOI

[Wo] Wolfart, J., Werte Hypergeometrischer Funktionen, Inv. Math. 92 (1988), 187-216. | EuDML | Zbl | DOI

[Wü] Wüstholz, G., Algebraische Punkte auf analytischen Untergruppen algebraischer Gruppen, Ann. Math. (1989), 501-517. | Zbl | DOI