Geodesic
Length of the Sum and Product of Algebraic Numbers
Matematičeskie zametki, Tome 77 (2005) no. 6, pp. 854-860

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In the present paper, we consider products of lengths of algebraic numbers whose sum or product is a chosen algebraic number. These products are used to construct a new height function for algebraic numbers. With the help of this function, a metric on the set of all algebraic numbers, which induces the discrete topology, is introduced. 
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     author = {A. Dubickas and C. Smyth},
     title = {Length of the {Sum} and {Product} of {Algebraic} {Numbers}},
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A. Dubickas; C. Smyth. Length of the Sum and Product of Algebraic Numbers. Matematičeskie zametki, Tome 77 (2005) no. 6, pp. 854-860. http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a4/