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Mat. Sb., 1999, Volume 190, Number 3, Pages 89–108 (Mi msb394)  

This article is cited in 6 scientific papers (total in 6 papers)

On the successive minima of the extended logarithmic height of algebraic numbers

E. M. Matveev

Moscow State Textile Academy named after A. N. Kosygin

Abstract: Suppose that $\mathbb K\subseteq\mathbb C$ is an algebraic field; $S=2$ if $\mathbb K$ is complex, and $S=1$ if $\mathbb K\subseteq\mathbb R$; $\delta=[\mathbb K:\mathbb Q]/S$. For $\alpha\in\mathbb K^*$ let $H_*(\alpha)=\max\{\delta h(\alpha),|\ln\alpha|\}$, where $h(\alpha)$ is the Weil height of the number $\alpha$. Then the inequality
$$ H_*(\alpha_1)\dotsb H_*(\alpha_n)2.5^n(e^{0.2n}n)^S\delta\ln(4.64\delta)>1 $$
holds for multiplicatively independent $\alpha_1,…,\alpha_n\in\mathbb K^*$.

DOI: https://doi.org/10.4213/sm394

Full text: PDF file (345 kB)
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English version:
Sbornik: Mathematics, 1999, 190:3, 407–425

Bibliographic databases:

UDC: 511
MSC: Primary 11R09, 11H06; Secondary 11J25, 11H31, 11J86
Received: 04.04.1997 and 10.03.1998

Citation: E. M. Matveev, “On the successive minima of the extended logarithmic height of algebraic numbers”, Mat. Sb., 190:3 (1999), 89–108; Sb. Math., 190:3 (1999), 407–425

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. E. M. Matveev, “An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II”, Izv. Math., 64:6 (2000), 1217–1269  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Amoroso F., “Une minoration pour l'exposant du groupe de classes d'idéaux [Lower bound for the exponent of the ideal class group]”, Acta Arith., 115:1 (2004), 59–69  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Loher Th., Masser D., “Uniformly counting points of bounded height”, Acta Arith., 111:3 (2004), 277–297  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. E. M. Matveev, “The index of multiplicative groups of algebraic numbers”, Sb. Math., 196:9 (2005), 1307–1318  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Yu. M. Alexencev, “Index of Lattices and Hilbert Polynomials”, Math. Notes, 80:3 (2006), 313–317  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Yu. M. Aleksentsev, “The Hilbert polynomial and linear forms in the logarithms of algebraic numbers”, Izv. Math., 72:6 (2008), 1063–1110  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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