The generalization improves inequality bounds for regulators in number fields, highlighting the role of conjugates.
We generalize an inequality conjectured by Pohst in 1977 and recently proved by the author and independently by Battistoni and Molteni. This new inequality improves a bound for the regulator in terms of the discriminant for totally real number fields by taking into account the signs of conjugates of a minimal unit. We give a new interpretation to the problem and exploit the combinatorial method used by Pohst.
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