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Approximation durch algebraische Zahlen beschränkten Grades im Körper der formalen laurentreihen

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Approximation by Algebraic Numbers of Bounded Degree in the Field of Formal Laurent Series. In this paper results ofWirsing andDavenport-Schmidt concerning the approximation of certain numbers by algebraic numbers of bounded degree are transferred to the field of formal power series connected with a certain non-archimedian valuation.

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Literaturverzeichnis

  1. Bosch, S., Güntzer, U., Remmert, R.: Non-Archimedian Valuation. Berlin-Heidelberg-New York-Tokyo: Springer. 1984.

    Google Scholar 

  2. Davenport, H., Schmidt, W. M.: Approximation to real numbers by quadratic irrationals. Acta Arith.13, 169–176 (1967).

    Google Scholar 

  3. Davenport, H., Schmidt, W. M.: A theorem on linear forms. Acta Arith.15, 209–223 (1968).

    Google Scholar 

  4. Geijsel, J. M.: Transcendence in fields of positive characteristic. Amsterdam. Academisch Proefschrift 1978.

    Google Scholar 

  5. Mahler, K.: An analogue to Minkowski's geometry of numbers in a field of series. Ann. of Math.42, 488–522 (1941).

    Google Scholar 

  6. Morrison, J. F.: Approximation ofp-adic numbers by algebraic numbers of bounded degree. J. Number Theory10, 334–350 (1978).

    Google Scholar 

  7. Ratliff, M.: The Thue-Siegel-Roth-Schmidt Theorem for algebraic functions. J. Number Theory10, 99–126 (1978).

    Google Scholar 

  8. Schneider, Th.: Einführung in die transzendenten Zahlen. Berlin-Göttingen-Heidelberg: Springer. 1957.

    Google Scholar 

  9. Sprindzuk, V. G.: On algebraic approximation in the field of power series. Vestnik Leningrad Univ. Ser. Mat. Meh. Astronom18/3, 130–134 (1963).

    Google Scholar 

  10. Sprindzuk, V. G.: Mahler's problem in metric number theory. Transl. of Math. Monographs Vol. 25. Providence R. I.: Amer. Math. Soc. 1969.

    Google Scholar 

  11. Wirsing, E.: Approximation mit algebraischen Zahlen beschränkten Grades. J. Reine Angew. Math.206, 67–77 (1960).

    Google Scholar 

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Guntermann, N. Approximation durch algebraische Zahlen beschränkten Grades im Körper der formalen laurentreihen. Monatshefte für Mathematik 122, 345–354 (1996). https://doi.org/10.1007/BF01326033

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  • DOI: https://doi.org/10.1007/BF01326033

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