An estimate of an incomplete linear form in several algebraic numbers

  • N. I. Fel'dman


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.


Linear Form Additional Condition Rational Number Algebraic Number Quadratic Field 
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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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