Abstract
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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Translated from Matematicheskie Zametki, vol. 77, no. 6, 2005, pp. 854–860.
Original Russian Text Copyright ©2005 by A. Dubickas, C. J. Smyth.
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Dubickas, A., Smyth, C.J. Length of the Sum and Product of Algebraic Numbers. Math Notes 77, 787–793 (2005). https://doi.org/10.1007/s11006-005-0079-y
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DOI: https://doi.org/10.1007/s11006-005-0079-y