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On metric heights

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Abstract

Metric heights are modified height functions on the non-zero algebraic numbers Q which can be used to define a metric on certain cosets of \(\overline {\mathbb{Q}} ^* \). They have been defined with a view to eventually applying geometric methods to the study of \(\overline {\mathbb{Q}} ^* \). In this paper we discuss the construction of metric heights in general. More specifically, we study in some detail the metric height obtained from the na"ve height of an algebraic number (the maximum modulus of the coefficients of its minimal polynomial). In particular, we compute this metric height for some classes of surds.

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REFERENCES

  1. A. Dubickas, Mahler measures close to an integer, Canadian Math. Bull. 45 (2002), 196–203.

    MATH  MathSciNet  Google Scholar 

  2. A. Dubickas and C. J. Smyth, On the Remak height, the Mahler measure, and conjugate sets of algebraic numbers lying on two circles, Proc. Edinburgh Math. Soc. 44 (2001), 1–17.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Dubickas and C. J. Smyth, On the metric Mahler measure, J. Number Th. 86 (2001), 368–387.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Waldschmidt, Diophantine Approximation on Linear Algebraic Groups, Springer-Verlag, Berlin, New York, 2000.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius, 2600, Lithuania E-mail

    A. Dubickas

  2. School of Mathematics, Edinburgh, University, J.C.M.B, King's Buildings Mayfield Road, Edinburgh, EH9 3JZ, Scotland, UK E-mail

    C. J. Smyth

Authors
  1. A. Dubickas
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  2. C. J. Smyth
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Dubickas, A., Smyth, C.J. On metric heights. Periodica Mathematica Hungarica 46, 135–155 (2003). https://doi.org/10.1023/A:1025936026150

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  • DOI: https://doi.org/10.1023/A:1025936026150

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