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Mat. Sb., 2005, Volume 196, Number 9, Pages 59–70 (Mi msb1420)  

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

The index of multiplicative groups of algebraic numbers

E. M. Matveev

Moscow State Textile Academy named after A. N. Kosygin

Abstract: Fix several non-zero elements of an algebraic field with linearly independent logarithms. Consider the set of elements of the field whose logarithms can be expressed in terms of the logarithms of the fixed numbers using rational coefficients. The corresponding vectors of coefficients make up a lattice with the standard integral lattice as a finite-index sublattice. An improved upper bound for this index is given in terms of the extended logarithmic heights of the quantities involved. On the way an estimate for the coefficients in integer linear relations between the logarithms of algebraic numbers is obtained.

DOI: https://doi.org/10.4213/sm1420

Full text: PDF file (272 kB)
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English version:
Sbornik: Mathematics, 2005, 196:9, 1307–1318

Bibliographic databases:

UDC: 511.36+511.61
MSC: Primary 11H06, 11J86; Secondary 11G50
Received: 05.03.2004

Citation: E. M. Matveev, “The index of multiplicative groups of algebraic numbers”, Mat. Sb., 196:9 (2005), 59–70; Sb. Math., 196:9 (2005), 1307–1318

Citation in format AMSBIB
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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. Vaaler J.D., “Heights on Groups and Small Multiplicative Dependencies”, Trans. Am. Math. Soc., 366:6 (2014), 3295–3323  crossref  mathscinet  zmath  isi
    2. Akhtari Sh., Vaaler J.D., “Heights, regulators and Schinzel's determinant inequality”, Acta Arith., 172:3 (2016), 285–298  crossref  mathscinet  zmath  isi  scopus
    3. Bugeaud Y., “Linear Forms in Logarithms and Applications”, Linear Forms in Logarithms and Applications, Irma Lectures in Mathematics and Theoretical Physics, 28, Eur. Math. Soc., 2018, 1–224  crossref  mathscinet  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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