A Detailed Proof of Pohst's Inequality

Abstract

In 1977 Pohst conjectured a certain inequality for $n$ variables and give a computer-assisted proof for $n\le 10$. We give a proof for all $n$ using a combinatorial argument. This inequality yields a better bound for the regulator in terms of the discriminant for totally real number fields.

arXiv comment12 pages, 9 figures