There are no universal ternary quadratic forms over biquadratic fields

DOI10.1017/S001309152000022XzbMath1460.11042arXiv1909.05422OpenAlexW3092554175MaRDI QIDQ4971953

Jakub Krásenský, Kristýna Zemková, Magdaléna Tinková

Publication date: 14 October 2020

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.05422

zbMATH Keywords

ternary quadratic formbiquadratic number fielduniversal quadratic formindecomposable integer

Mathematics Subject Classification ID

General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Quadratic forms over global rings and fields (11E12) Algebraic numbers; rings of algebraic integers (11R04) Totally real fields (11R80)

Related Items (8)

On indefinite \(k\)-universal integral quadratic forms over number fields ⋮ Lifting problem for universal quadratic forms over totally real cubic number fields ⋮ Trace and norm of indecomposable integers in cubic orders ⋮ Lifting problem for universal quadratic forms ⋮ Composition of binary quadratic forms over number fields ⋮ Real quadratic fields admitting universal lattices of rank 7 ⋮ Pythagoras numbers of orders in biquadratic fields ⋮ Number fields without universal quadratic forms of small rank exist in most degrees

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