Pythagoras number of quartic orders containing √(2)

2022/04/22 by Zilong He, Yong Hu, He, Zilong +1
Computer Science · Mathematics · #11E12 #11E16 #11E25 #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2204.10468

openalex publication_date 2022/04/22 · openalex created_date 2022/04/27 · openalex updated_date 2026/07/28

Abstract

Let K be a quartic number field containing √(2) and let O⊆ K be an order such that √(2)∈ O. We prove that the Pythagoras number of O is at most 5. This confirms a conjecture of Krásenský, Raška and Sgallová. The proof makes use of Beli's theory of bases of norm generators for quadratic lattices over dyadic local fields.

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