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On dense sequences of polynomials in several variables

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Abstract

In the present paper a form of generalization of Gelfond's lemma on dense sequences of polynomials is proposed. For a set of complex numbersθ 1, ...,θ s we define the coefficientsgk(θ 1, ...,θ s ) (0⩽k⩽s) and give the relations between them and the transcendental degrees or the transcendence types of the field © (θ 1, ...,θ s ) or its subfields.

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References

  1. Gelfond, A. O., Transcendental and algebraic numbers, Dover Pub., Inc., New York, 1960.

    Google Scholar 

  2. Tijdeman, R., On the algebraic independence of certain numbers,Indag. Math.,33 (1971), 146–162

    Google Scholar 

  3. Chudnovsky, G. V., Contributions to the theory of transcendental numbers, AMS Math. Surveys & Monographs, No. 19, Providence, 1984.

  4. Reyssat, E., Un critère d' indépendance algébrique,J. Rei. Angew. Math.,329 (1981), 66–81.

    Google Scholar 

  5. Waldschmidt, M. et Zhu, Y. C., Une généralisation en plusieurs variables d ' un critère de transcendance de Gelfond,C. R. Acad. Sc. Paris, Sér. I,297 (1983), 229–232.

    Google Scholar 

  6. Zhu, Y. C., Criteria of algebraic independence of complex numbers over a field of finite transcendence type,Kexue Tongbao,34 (1989), 185–189.

    Google Scholar 

  7. Waldschmidt, M., Groupes algébriques et grands degrés de transcendance,Acta Math.,156 (1986), 253–302.

    Google Scholar 

  8. Lang, S., Introduction to transcendental numbers, Addison-Wesley, Reading, Mass., 1966.

    Google Scholar 

  9. Zhu, Y. C., A generalization in several variables of a transcendence creterion of Gelfond (II),Scientia Sinica, Ser. A,31 (1988), 897–907.

    Google Scholar 

  10. Waldschmidt, M., Nombres Transcendants, LNM No. 402, Springer-Verlag, Berlin-Heidberg-New York, 1974.

    Google Scholar 

  11. Philippon, P., Critères pour l'indépendance algégrique, IHES Pub. Notes, No. 64, 1987.

  12. Nesterenko, Yu. V., Order function for almost all numbers,Math. Notes,15 (1974), 234–240.

    Google Scholar 

  13. Atiyah, M. F. & MacDonald, I. G., Introduction to commutative algevra, Addison-Wesley, Reading, Mass., 1969.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academia Sinica, China

    Zhu Yaochen

Authors
  1. Zhu Yaochen
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Additional information

This work was completed at the Dept. of Math., Univ. of Southern Mississippi, USA in 1987.

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Yaochen, Z. On dense sequences of polynomials in several variables. Acta Mathematica Sinica 5, 329–336 (1989). https://doi.org/10.1007/BF02107710

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  • DOI: https://doi.org/10.1007/BF02107710

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