On the Pythagoras number of the simplest cubic fields
Volume 208 / 2023
Acta Arithmetica 208 (2023), 325-354
MSC: Primary 11R16; Secondary 11E25, 11R80.
DOI: 10.4064/aa221003-27-6
Published online: 28 August 2023
Abstract
Let $\rho $ be a root of the polynomial $x^3-ax^2-(a+3)x-1$ where $a\geq 3$. We show that the Pythagoras number of the order $\mathbb Z[\rho ]$ is equal to $6$.
