Computing the Length of Sum of Squares and Pythagoras Element in a Global Field
Number Theory
2023-06-22 v2
Abstract
This paper presents algorithms for computing the length of a sum of squares and a Pythagoras element in a global field of characteristic different from . In the first part of the paper, we present algorithms for computing the length in a non-dyadic and dyadic (if is a number field) completion of . These two algorithms serve as subsidiary steps for computing lengths in global fields. In the second part of the paper we present a procedure for constructing an element whose length equals the Pythagoras number of a global field, termed a Pythagoras element.
Keywords
Cite
@article{arxiv.2102.08741,
title = {Computing the Length of Sum of Squares and Pythagoras Element in a Global Field},
author = {Mawunyo Kofi Darkey-Mensah and Beata Rothkegel},
journal= {arXiv preprint arXiv:2102.08741},
year = {2023}
}