Abstract
In a recent paper I generalized the Thue-Siegel-Roth-Schmidt theorem on simultaneous rational approximation of n real algebraic numbers to include also the p-adic case. In the present paper I shall carry the argument further and prove analogous results for systems of real and p-adic linear forms with algebraic coefficients.
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Literatur
AITKEN, A.C., Determinants and matrices, Oliver and Boyd, London (1951)
CASSELS, J.W.S. An introduction to the geometry of numbers, Springer Berlin-Göttingen-Heidelberg (1959)
LUTZ, E. Sur les approximations diophantiennes linéaires p-adiques, Hermann Paris (1955)
MAHLER, K. Über diophantische Approximationen im Gebiete der p-adischen Zahlen Jahresbericht der DMV44 (1934), 250–255
— Ein Übertragungsprinzip für lineare Ungleichungen, Casopis.Pest.Mat.68 (1939), 85–92
— On compound convex bodies (I), Proc.London Math.Soc.Ser.III,5 (1955), 358–379
RIDOUT, D. The p-adic generalization of the Thue-Siegel-Roth theorem, Mathematika5 (1958), 40–48
ROTH, K.F. Rational approximations to algebraic numbers, Mathematika2 (1955), 1–20
SCHLICKEWEI, H.P. Die p-adische Verallgemeinerung des Satzes von Thue-Siegel-Roth-Schmidt, Journ.R.Ang.Math. (erscheint demnächst)
SCHMIDT, W.M. On simultaneous approximation of two algebraic numbers by rationals Acta Math.119 (1967), 27–50
SCHMIDT, W.M. Simultaneous approximation to algebraic numbers by rationals Acta Math.125 (1970), 189–201
— Linear forms with algebraic coefficients I J. of Number Theory3 (1971), 253–277
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Schlickewei, H.P. Linearformen mit algebraischen Koeffizienten. Manuscripta Math 18, 147–185 (1976). https://doi.org/10.1007/BF01184304
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DOI: https://doi.org/10.1007/BF01184304