A Refinement of Pohst's Inequality

TL;DR

This paper generalizes Pohst's inequality, providing a tighter bound for the regulator of totally real number fields by incorporating conjugate signs, using combinatorial methods for improved analysis.

Contribution

It introduces a refined inequality that improves bounds on the regulator by considering conjugate signs, extending Pohst's original conjecture and proof.

Findings

New inequality for regulators of totally real fields

Enhanced bounds considering conjugate signs

Application of combinatorial methods to number theory

Abstract

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 the fundamental unit. We give a new interpretation to the problem and exploit the combinatorial method used by Pohst.