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A note on a problem of Baker in metrical number theory

Published online by Cambridge University Press:  24 October 2008

Kunrui Yu
Kunrui Yu
Affiliation:
Institute of Mathematics, Chinese Academy of Sciences, Peking
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Extract

Let P(x) denote a polynomial with degree n and integer coefficients. By the height h of P we mean the maximum of the absolute values of the coefficients.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 2 , September 1981 , pp. 215 - 227
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

REFERENCES

(1)Baker, A.On some Diophantine inequalities involving the exponential function. Canadian J. Math. 17 (1965), 616–626.CrossRefGoogle Scholar
(2)Baker, A.On a theorem of Sprindžuk. Proc. Roy. Soc. London A 292 (1966), 92–104.Google Scholar
(3)Baker, A.Transcendental number theory (CambridgeUniversity Press, 1975).CrossRefGoogle Scholar
(4)Baker, A. and Schmidt, W. M.Diophantine approximation and Hausdorff dimension. Proc. London Math. Soc. 21 (1970), 1–11.CrossRefGoogle Scholar
(5)Besicovitch, A. S.Sets of fractional dimensions (IV): On rational approximation to real numbers. J. London Math. Soc. 9 (1934), 126–131.CrossRefGoogle Scholar
(6)Cassels, J. W. S.An introduction to Diophantine approximation (Cambridge University Press, 1957).Google Scholar
(7)Davenport, H.A note on binary cubic forms. Mathematika 8 (1961), 58–62.CrossRefGoogle Scholar
(8)Jabník, V.Diophantische Approximationen und Hausdorffsches Mass. Mat. Sb. 36 (1929), 371–382.Google Scholar
(9)Kasch, F.Über eine metriuche Eigenschaft der S-Zahlen. Math. Zeit. 70 (1958), 263–270.Google Scholar
(10)Khintchine, A. Ya. [Khinchin, A. YA.] Continued fractions (Chicago University Press, 1964).Google Scholar
(11)Schmidt, W. M.Metrische Sätze über simultane Approximation abhängiger Grössen. Monatsh. Math. 68 (1964), 154–166.CrossRefGoogle Scholar
(12)Schneider, Th.Einführung in die transzendenten Zahlen (Springer Verlag, Berlin, Göttingen, Heidelberg, 1957).CrossRefGoogle Scholar
(13)Sprindžuk, V. G.Proof of the conjecture of Mahler on the measure of the set of S-numbers. Izv. Akad. Nauk SSSR (ser. mat.) 29 (1965), 379–436 (in Russian).Google Scholar
(14)Sprindžuk, V. G.Metric theory of diophantine approximations, Current problems of analytic number theory. In Proc. Summer School on Analytic Number Theory, Minsk, 1972, 178–198, (Izd. Nauka i Tekhnika, Minsk, 1974) (in Russian).Google Scholar
(15)Sprindžuk, V. G.Metric theory of diophantine approximations (V. H. Winston, Washington, D.C., 1979).Google Scholar
(16)Volkmann, B.Zur Mahlerschen Vermutung im Komplexen. Math. Ann. 140 (1960), 351–359.CrossRefGoogle Scholar
(17)Volkmann, B.The real cubic case of Mahler's conjecture. Mathematika 8 (1961), 55–57.CrossRefGoogle Scholar
(18)Wang, Y., Yu, K. R. and Zhu, Y. C.On a transference theorem on linear forms. Acta Math. Sinica 22 (1979), 237–240.Google Scholar