Bounds on the Pythagoras number and indecomposables in biquadratic fields

2023/11/28 by Magdaléna Tinková, Tinková, Magdaléna · 1 citation
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2311.16660

openalex publication_date 2023/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for all real biquadratic fields not containing √(2), √(3), √(5), √(6), √(7), and √(13), the Pythagoras number of the ring of algebraic integers is at least 6. We will also provide an upper bound on the norm and the minimal (codifferent) trace of additively indecomposable integers in some families of these fields.

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