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Mat. Zametki, 2002, Volume 72, Issue 6, Pages 828–833 (Mi mz470)  

This article is cited in 3 scientific papers (total in 3 papers)

Certain Diophantine Properties of the Mahler Measure

A. Dubickas

Vilnius University

Abstract: It is proved that a polynomial in several Mahler measures with positive rational coefficients is equal to an integer if and only if all these Mahler measures are integers. An estimate for the distance between a metric Mahler measure and an integer is obtained. Finally, it is proved that the ratio of two distinct Mahler measures of algebraic units is irrational.

DOI: https://doi.org/10.4213/mzm470

Full text: PDF file (171 kB)
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English version:
Mathematical Notes, 2002, 72:6, 763–767

Bibliographic databases:

UDC: 511
Received: 27.06.2001
Revised: 26.02.2002

Citation: A. Dubickas, “Certain Diophantine Properties of the Mahler Measure”, Mat. Zametki, 72:6 (2002), 828–833; Math. Notes, 72:6 (2002), 763–767

Citation in format AMSBIB
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\paper Certain Diophantine Properties of the Mahler Measure
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\pages 828--833
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\pages 763--767
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Dubickas A., “On numbers which are Mahler measures”, Monatsh. Math., 141:2 (2004), 119–126  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Wu Q., “The Smallest Perron Numbers”, Math. Comput., 79:272 (2010), 2387–2394  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Friedl S., “Commensurability of Knots and l-2-Invariants”, Geometry and Topology Down Under, Contemporary Mathematics, 597, eds. Hodgson C., Jaco W., Scharlemann M., Tillmann S., Amer Mathematical Soc, 2013, 263–279  crossref  zmath  isi
  • Математические заметки Mathematical Notes
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