Abstract
LetPn(y1,…,yn):=∏1≤i<j≤n(1−yiyj) andPn:=sup(y1,…,yn)Pn(y1,…,yn) where the supremum is taken over the n-ples (y1,…,yn) of real numbers satisfying 0<|y1|<|y2|<⋯<|yn|. We prove that Pn≤2⌊n/2⌋ for every n, i.e., we extend to all n the bound that Pohst proved for n≤11. As a consequence, the bound for the absolute discriminant of a totally real field in terms of its regulator is now proved for every degree of the field.
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