Number fields without universal quadratic forms of small rank exist in most degrees

DOI10.1017/S0305004122000214MaRDI QIDQ5877286

Vítězslav Kala

Publication date: 10 February 2023

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

Full work available at URL: https://arxiv.org/abs/2101.10364

Mathematics Subject Classification ID

Other number fields (11R21) General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Quadratic forms over global rings and fields (11E12) Totally real fields (11R80)

Related Items (2)

Can we recover an integral quadratic form by representing all its subforms? ⋮ Real quadratic fields admitting universal lattices of rank 7

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Universal octonary diagonal forms over some real quadratic fields.
• Universal quadratic forms over multiquadratic fields
• On the rank of universal quadratic forms over real quadratic fields
• Real quadratic fields admitting universal lattices of rank 7
• Squarefree values of polynomial discriminants. I
• Lifting problem for universal quadratic forms
• A lower bound for the rank of a universal quadratic form with integer coefficients in a totally real number field
• Sums of \(m\)th powers of algebraic integers
• A construction of polynomials with squarefree discriminants
• UNIVERSAL QUADRATIC FORMS AND ELEMENTS OF SMALL NORM IN REAL QUADRATIC FIELDS
• The Simplest Cubic Fields
• Representations of positive definite quadratic forms.
• Universal positive quaternary quadratic lattices over totally real number fields
• A finiteness theorem for representability of quadratic forms by forms
• There are no universal ternary quadratic forms over biquadratic fields
• Number fields without n-ary universal quadratic forms
• Universal quadratic forms and indecomposables over biquadratic fields
• Universality of a non-classical integral quadratic form over Q ( \sqrt 5 )

This page was built for publication: Number fields without universal quadratic forms of small rank exist in most degrees