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. Smyth , C. J. 2001 On the metric Mahler measure J. Number Theory 86 368 – 387 10.1006/jnth.2000.2579 . [4

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We investigate the values of the Remak height, which is a weighted product of the conjugates of an algebraic number. We prove that the ratio of logarithms of the Remak height and of the Mahler measure for units αof degree d is everywhere dense in the maximal interval [d/2(d-1),1] allowed for this ratio. To do this, a “large” set of totally positive Pisot units is constructed. We also give a lower bound on the Remak height for non-cyclotomic algebraic numbers in terms of their degrees. In passing, we prove some results about some algebraic numbers which are a product of two conjugates of a reciprocal algebraic number.

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measure and conjugate sets of algebraic numbers lying on two circles, Proc. Edinburgh Math. Soc. 44 (2001), 1–17. MR 2003a :11136 Smyth C. J. On the Remak height, the Mahler

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