On the Pythagoras number of the simplest cubic fields

Abstract

The simplest cubic fields $\mathbb{Q}(\rho )$ are generated by a root $\rho$ of the polynomial $x^3-a{x}^2-(a+3)x-1$ where $a\ge -1$. In this paper, we will show that the Pythagoras number of the order $\mathbb{Z}[\rho ]$ is equal to $6$ for $a\ge 3$.

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• Lifting problem for universal quadratic forms
• Universal quadratic forms, small norms and traces in families of number fields
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Cited by in corpus (7)

• Universal quadratic forms, small norms and traces in families of number fields
• On Kitaoka's conjecture and lifting problem for universal quadratic forms
• Pythagoras numbers of orders in biquadratic fields
• Universal quadratic forms and indecomposables in number fields: A survey
• Additive structure of non-monogenic simplest cubic fields
• Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables
• Pythagoras numbers for infinite algebraic fields