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Creators/Authors contains: "Ted Chinburg, Eduardo Friedman"

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  1. (, Pacific journal of mathematics)
    Let L be a number field and let E ⊂ OL∗ be any subgroup of the units of L. If rankZ(E) = 1, Lehmer’s conjecture predicts that the height of any non-torsion element of E is bounded below by an absolute positive constant. If rankZ(E) = rankZ(OL∗), Zimmert proved a lower bound on the regulator of E which grows exponentially with [L : Q]. By sharpening a 1997 conjecture of Daniel Bertrand’s, Fernando Rodriguez Villegas “interpolated” between these two extremes of rank with a new higher-dimensional version of Lehmer’s conjecture. Here we prove a high-rank case of the Bertrand-Rodriguez Villegas conjecture. Namely, it holds if L contains a subfield K for which [L : K] ≫ [K : Q] and E contains the kernel of the norm map from OL∗ to OK∗ . 
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