## On the Thue-Siegel-Dyson theorem.(English)Zbl 0505.10015

### MSC:

 11J68 Approximation to algebraic numbers

### Citations:

Zbl 0030.02101; Zbl 0090.261; Zbl 0222.10036
Full Text:

### References:

 [1] Baker, A., Rational approximation to $$\sqrt[3]{2}$$ and other algebraic numbers.Quart. J. Math. Oxford, 15 (1964), 375–383. · Zbl 0222.10036 [2] – Simultaneous rational approximations to certain algebraic numbers.Proc. Camb. Phil. Soc., 63 (1967), 693–702. · Zbl 0166.05503 [3] Baker, A. The theory of linear forms in logarithms. InTranscendence Theory: Advances and Applications. Baker, A., & Masser, D. W. ed. Academic Press 1977. · Zbl 0361.10028 [4] Baker, A. Recent advances in transcendence theory.Proceedings of International Conference on Number Theory, Moscow 1971, 67–69. [5] Bombieri, E., On G-functions. InRecent Progress in Analytic Number Theory, vol II. H. Halberstam & C. Hooley ed., Academic Press 1981. [6] Dyson, F., The approximation to algebraic numbers by rationals.Acta Math., 79 (1947), 225–240. · Zbl 0030.02101 [7] Feldman, N. I.. An effective refinement of the exponent in Liouville’s theorem (Russian).Izv. Akad. Nauk SSSR Ser. Mat., 35 (1971), 973–990. AlsoMath. USSR-Izv., 5 (1971), 985–1002. [8] Gelfond, A. O.,Transcendental and algebraic numbers. English translation by L. F. Boron. Dover Publications Inc., New York 1960. · Zbl 0090.26103 [9] Hyyrö, S., Über rationale Näherungswerte algebraischer Zahlen,Ann. Acad. Sci. Fenn. Ser. A. I. Math., 376 (1965), 1–15. · Zbl 0131.04801 [10] Lang, S.,Diophantine geometry. Interscience Publishers Inc., New York-London 1962. · Zbl 0115.38701 [11] Mahler, K., Inequalities for ideal bases in algebraic number fields.J. Austral. Math. Soc., IV (1964), 425–448. · Zbl 0218.12004 [12] Stark, H. M., An explanation of some exotic continued fractions found by Brillhart.Computers in Number Theory (Proc. Sci. Res. Council Atlas Symp. No. 2 Oxford 1969), pp. 21–35. Academic Press, London 1971. [13] Thue, A.,Selected mathematical papers. Universitet-forlaget Oslo-Bergen-Tromsø, 1977. · Zbl 0359.01021 [14] Weil, A., Arthmetic on algebraic varieties.Ann. of Math., 53 (1951), 412–444. · Zbl 0043.27002
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