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The transcendence of certain quasi-periods associated with Abelian functions in two variables. (English) Zbl 0371.10026

MSC:
11J81 Transcendence (general theory)
14K25 Theta functions and abelian varieties
32A20 Meromorphic functions of several complex variables
33E05 Elliptic functions and integrals
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References:
[1] A. Baker : On the quasi-periods of the Weierstrass \zeta -function . Göttinger Nachr. (1969) No. 16, 145-157. · Zbl 0201.05403
[2] N.I. Feldman : Estimate for a linear form in logarithms of algebraic numbers . Mat. Sbornik 76 (1968) 304-319 (Math. USSR Sbornik 5 (1968) 291-307). · Zbl 0195.33701 · doi:10.1070/SM1968v005n02ABEH001007
[3] S. Lang : Transcendental points on group varieties . Topology 1 (1962) 313-318. · Zbl 0116.38105 · doi:10.1016/0040-9383(62)90018-6
[4] D.W. Masser : Elliptic functions and transcendence . Springer Lecture Notes in Math. No. 437, Berlin, 1975. · Zbl 0312.10023
[5] D.W. Masser : Linear forms in algebraic points of Abelian functions I . Math. Proc. Cambridge Philos. Soc. 77 (1975) 499-513. · Zbl 0306.14018 · doi:10.1017/S030500410005132X
[6] D.W. Masser : On the periods of Abelian functions in two variables . Mathematika 22 (1975) 97-107. · Zbl 0318.14010 · doi:10.1112/S0025579300005933
[7] D.W. Masser : Some vector spaces associated with two elliptic functions, to appear in Transcendence theory advances and applications . Academic Press, London and New York, 1977. · Zbl 0362.10029
[8] Th. Schneider : Zur Theorie der Abelschen Funktionen und Integrale . J. reine angew. Math. 183 (1941) 110-128. · Zbl 0024.15504 · doi:10.1515/crll.1941.183.110 · eudml:183486
[9] C.L. Siegel : Topics in complex function theory , Vol. III. Wiley-Interscience, New York, 1973. · Zbl 0184.11201
[10] M. Waldschmidt : Nombres transcendants . Springer Lecture Notes in Math. 402, 1974. · Zbl 0302.10030
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