Geodesic
On linear and multiplicative relations
Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 411-425 Cet article a éte moissonné depuis la source Math-Net.Ru

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A theorem on the successive minima of lattices corresponding to the integer solutions of systems of linear equations is proved. As a corollary, theorems on the successive minima are obtained for the set of solutions of equations of the form $$ x_1\ln\alpha_1+\dots+x_n\ln\alpha_n=\ln\beta, \qquad x_1,\dots,x_n\in\mathbb{Z}, $$ for fixed $\alpha_1,\dots,\alpha_n$ in an algebraic number field $\mathbb{K}$ and for variable $\beta\in\mathbb{K}$ equal either to 1 or a root of unity. 
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     author = {E. M. Matveev},
     title = {On linear and multiplicative relations},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_2_a8/}
}
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E. M. Matveev. On linear and multiplicative relations. Sbornik. Mathematics, Tome 78 (1994) no. 2, pp. 411-425. http://geodesic.mathdoc.fr/item/SM_1994_78_2_a8/

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