A Refinement of Pohst's Inequality
Number Theory
2025-09-23 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.2212.01500,
title = {A Refinement of Pohst's Inequality},
author = {Gabriel Raposo},
journal= {arXiv preprint arXiv:2212.01500},
year = {2025}
}
Comments
21 pages, 15 figures