On the effective Pourchet's Theorem
Number Theory
2025-11-18 v1 Commutative Algebra
Abstract
With the aid of Hensel Lemma, we refine the 2-adic Newton polygon algorithm proposed by Magron, Koprowski, and Vaccon at ISSAC 2023 to express computationally a given positive univariate polynomial with rational coefficients as a sum of five squares of rational polynomials -the effective Pourchet's Theorem- and extend it to cover almost all the possible inputs. We also provide examples which are covered with our methods but cannot be detected by previous conjectural algorithms.
Cite
@article{arxiv.2511.11783,
title = {On the effective Pourchet's Theorem},
author = {Teresa Cortadellas Benitez and Carlos D'Andrea and Ana Belen de Felipe and Joel Hurtado Moreno and M. Eulalia Montoro},
journal= {arXiv preprint arXiv:2511.11783},
year = {2025}
}
Comments
12 pages, latex