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We survey the known results and open questions related to the Lehmer Problem. We start by recalling the "classical" conjecture : the existence of a lower bound for the height of an algebraic number (not a root of unity) of the form h() c Q():Q and the generalizations to higher dimension. We discuss afterwards, the "relative" versions of these problems, that is, replacing de degree of over Q by the degree over Q ab . We give the most recent results on these questions and we discuss briefly an application of the latest to the Pink-Zilber conjecture.
María Carrizosa (Wed,) studied this question.
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