×

zbMATH — the first resource for mathematics

Diophantine approximation on Abelian varieties with complex multiplication. (English) Zbl 0306.14019

MSC:
14K22 Complex multiplication and abelian varieties
14G99 Arithmetic problems in algebraic geometry; Diophantine geometry
14K05 Algebraic theory of abelian varieties
33E05 Elliptic functions and integrals
11J17 Approximation by numbers from a fixed field
11J81 Transcendence (general theory)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Altman, A, The size function on abelian varieties, Trans. amer. math. soc., 164, 153-161, (1972) · Zbl 0244.14013
[2] Baker, A, Linear forms in the logarithms of algebraic numbers, Mathematika, 13, 204-216, (1966) · Zbl 0161.05201
[3] Baker, A, On the periods of the Weierstrass & function, (), 155-174
[4] Baker, A, An estimate for the &-function at an algebraic point, Amer. J. math., XVII, 619-622, (1970) · Zbl 0208.30901
[5] Bombieri, E, Algebraic values of meromorphic maps, Invent. math., 10, 267-287, (1970) · Zbl 0214.33702
[6] Bombieri, E; Lang, S, Analytic subgroups of group varieties, Invent. math., 11, 1-14, (1970) · Zbl 0237.14015
[7] Coates, J, An application of the division theory of elliptic functions to Diophantine approximation, Invent. math., 11, 167-182, (1970) · Zbl 0216.04403
[8] Coates, J, Linear forms in the periods of the exponential and elliptic functions, Invent. math., 12, 290-299, (1971) · Zbl 0217.04001
[9] Davenport, H, Analytic methods for Diophantine equations and Diophantine inequalities, () · Zbl 1089.11500
[10] Feldman, N, An elliptic analogue of an inequality of Gelfond, Trans. Moscow math. soc., 18, 71-84, (1968)
[11] Lang, S, Diophantine geometry, (1962), Interscience New York · Zbl 0115.38701
[12] Lang, S, Transcendental points on group varieties, Topology, 1, 313-318, (1962) · Zbl 0116.38105
[13] Lang, S, Algebraic values of meromorphic functions, Topology, 3, 183-191, (1962) · Zbl 0133.13804
[14] Lang, S, Algebraic values of meromorphic functions II, Topology, 5, 363-370, (1966) · Zbl 0168.19002
[15] Lang, S, Diophantine approximations on toruses, Amer. J. math., 86, 521-533, (1964) · Zbl 0142.29601
[16] Lang, S, Introduction to transcendental numbers, (1966), Addison Wesley Reading, Mass · Zbl 0144.04101
[17] \scS. Lang, Les formes bilinéaires de Néron et Tate. Séminaire Bourbaki, 1963-1954, No. 274.
[18] Lang, S, Introduction to Diophantine approximation, (1966), Addison Wesley Reading, Mass
[19] Lang, S, Abelian varieties, (1958), Interscience New York · Zbl 0098.13201
[20] Lang, S, Introduction to algebraic and abelian functions, (1972), Addison Wesley Reading, Mass · Zbl 0255.14001
[21] Lang, S, Integral points on curves, Pub. math. IHES, (1960), Paris · Zbl 0112.13402
[22] \scD. Masser, Transcendence properties of elliptic functions, to appear. · Zbl 0312.10023
[23] \scD. Masser, Algebraic points of an elliptic function, to appear. · Zbl 0306.14018
[24] \scD. Masser, Polynomials in many variables, to appear. · Zbl 0436.32005
[25] Néron, A, Quasi-fonctions et hauteurs sur LES variétés abéliennes, Ann. math., 82, 249-331, (1965) · Zbl 0163.15205
[26] Schmidt, W, Lectures on Diophantine approximation, (1970), Univ. of Colorado
[27] Schneider, T, Zur theorie der abelschen funktionen und integrale, J. reine angew. math., 110-128, (1941) · JFM 67.0147.02
[28] Shimura, G, Complex multiplication of abelian varieties, Publ. math. soc. Japan, (1961)
[29] Stoll, W, Normal families of non-negative divisors, Math. zeitschr., 84, 154-218, (1964) · Zbl 0126.09702
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.