Geodesic
Rational approximations to algebraic numbers
Izvestiya. Mathematics , Tome 5 (1971) no. 5, pp. 1003-1019.

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In this article we derive a new effective estimate of rational approximations to algebraic numbers simultaneously in an Archimedian and several non-Archimedian metrics. 
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V. G. Sprindzhuk. Rational approximations to algebraic numbers. Izvestiya. Mathematics , Tome 5 (1971) no. 5, pp. 1003-1019. http://geodesic.mathdoc.fr/item/IM2_1971_5_5_a2/

[1] Sprindzhuk V. G., “Novoe primenenie $p$-adicheskogo analiza k predstavleniyam chisel binarnymi formami”, Izv. AN SSSR. Ser. matem., 34 (1970), 1038–1063 | Zbl

[2] Sprindzhuk V. G., “Effektivnaya otsenka ratsionalnykh priblizhenii k algebraicheskim chislam”, Dokl. AN BSSR, 14:8 (1970), 681–684 | Zbl

[3] Chebotarev N. G., Osnovy teorii Galua, ch. II, ONTI, M., L., 1937

[4] Chebotarev N. G., Sobr. soch., AN SSSR, M., L., 1949

[5] Baker A., “Contributions to the theory of Diophantine equation. I. On the representation of integers by binary forms”, Philos. Trans. Royal. Soc. London(A), 263:1139 (1968), 173–191 | DOI | MR | Zbl

[6] Coates J., “An effective $p$-adic analogue of a theorem of Thue”, Acta Arithmetica, 15 (1969), 279–305 | MR | Zbl

[7] Frobenius G., “Über Bezeihungen zwischen den Primidealen eines algebraische Körpers und die Substitutionen seiner Gruppe”, Sitzber. Berl. Akad., 1896, 689–705

[8] Liouville J., “Sur des classes très étendues de quantites dont la valeur n'est ni algebrique, ni même reductible à des irrationnelles algebriques”, Comptes rendus, 18 (1844), 883–885, 910–911; J. Math. pures et appl., 16 (1851), 133–142

[9] Ridout D., “The $p$-adic generalization of the Thue–Siegel–Roth Theorem”, Mathematika, 5 (1958), 40–48 | MR | Zbl

[10] Roth K. F., “Rational approximations to algebraic numbers”, Mathematika, 2 (1955), 1–20 and 168 | MR | Zbl