Geodesic
On a~measure of algebraic independence of values of an elliptic function
Izvestiya. Mathematics , Tome 59 (1995) no. 4, pp. 815-838.

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An estimate is obtained for a measure of algebraic independence of values of a Weierstrass elliptic function with algebraic invariants at various algebraic points. The estimate is sharp as a function of the degree and height of polynomials. 
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Yu. V. Nesterenko. On a~measure of algebraic independence of values of an elliptic function. Izvestiya. Mathematics , Tome 59 (1995) no. 4, pp. 815-838. http://geodesic.mathdoc.fr/item/IM2_1995_59_4_a7/

[1] Nesterenko Yu. V., “Ob algebraicheskoi nezavisimosti algebraicheskikh stepenei algebraicheskikh chisel”, Matem. sb., 123 (165):4 (1984), 435–459 | MR | Zbl

[2] Nesterenko Yu. V., “O mere algebraicheskoi nezavisimosti znachenii nekotorykh funktsii”, Matem. sb., 128 (170):4 (1985), 545–568 | MR | Zbl

[3] Nesterenko Yu. V., “O mere algebraicheskoi nezavisimosti znachenii ellipticheskikh funktsii v algebraicheskikh tochkakh”, UMN, 40:4 (1985), 221–222 | MR | Zbl

[4] Nesterenko Yu. V., “O stepeni transtsendentnosti nekotorykh polei, porozhdennykh znacheniyami eksponentsialnoi funktsii”, Mat. zametki, 46:3 (1989), 40–49 | MR

[5] Anderson M., Linear forms in algebraic points of an elliptic function, Thesis, Univ. of Nottingham, 1978, P. 120

[6] Brownawell W. D., Masser D. W., “Multiplicity estimates for analytic functions, I”, J. Reine Angew. Math., 313 (1980), 200–216 | MR

[7] Chudnovsky G. V., “Algebraic independence of the values of elliptic functions at algebraic points; Elliptic analogue of the Lindemann–Weierschtrass theorem”, Inventiones Math., 61 (1980), 267–290 | DOI | MR | Zbl

[8] Chudnovsky G. V., Contributions to the theory of transcendental numbers, AMS Mathematical surveys and Monographs, 19, Springer, 1984 | MR

[9] Diaz G., “Grands degres de transcendance pour des familles d'exponentielles”, J. Number Theory, 31 (1989), 1–23 | DOI | MR | Zbl

[10] Jabbouri E. M., “Mesures d'independance algebrique de valeurs de fonctions elliptiques et abeliennes”, C. R. Acad. Sc. Paris Ser. 1, 303:9 (1986) | MR | Zbl

[11] Lang S., Introduction to transcendental numbers, Addison–Wesley, 1966 | MR

[12] Masser D. W., Elliptic functions and transcendence, Lecture Notes in Math., 437, 1975 | MR | Zbl

[13] Masser D. W., Wüstholz G., “Fields of large transcendence degree generated by values of elliptic functions”, Invent. Math., 72 (1983), 407–464 | DOI | MR | Zbl

[14] Nesterenko Yu. V., “On a measure of algebraic independence of the values of elliptic functions”, Diophantine Approximations and Transcendental Numbers, Proceedings of the Colloquium C.I.R.M. (Luminy, 1990), ed. P. Philippon, Walter de Gruyter, Berlin–New York, 1992, 239–248 | MR

[15] Philippon P., “Varietes abeliennes et independance algebrique, II”, Inventiones Math., 72 (1983), 389–405 | DOI | MR | Zbl

[16] Philippon P., “Criteres pour l'independance algebrique”, Publ. Math. Inst. Hautes Etudes Sci., 1986, no. 64, 5–52 | DOI | MR | Zbl

[17] Ramachandra K., “Contributions to the theory of transcendental numbers, II”, Acta Arithmetica, XIV, 1968, 73–88 | MR | Zbl

[18] Wüstholz G., “Recent progress in transcendence theory”, Lecture Notes in Math., 1068, 1984, 280–296 | MR | Zbl

[19] Wüstholz G., “Über das abelsche Analogon des Lindemannschen Satzes”, Inventiones Math., 72 (1983), 363–388 | DOI | MR | Zbl