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An estimate of an incomplete linear form in several algebraic numbers

  • N. I. Fel'dman
Article

Abstract

Letμ>m−1, letν be a rational number, and letωk=b k v , where bk ≠ 0 are distinct numbers of an imaginary quadratic field K, which satisfy some additional conditions. Then
$$\begin{gathered} |{}_1x_1 \omega _1 + ... + x_m \omega _m | > X^{ - \mu } , \hfill \\ X = \max |x_k | \geqslant X, > 0, \hfill \\ 1 \leqslant k \leqslant m \hfill \\ \end{gathered}$$
where x1, ..., xm are integers of the field K, and X0 is an effective constant.

Keywords

Linear Form Additional Condition Rational Number Algebraic Number Quadratic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature cited

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Copyright information

© Consultants Bureau 1970

Authors and Affiliations

  • N. I. Fel'dman
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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