Universal quadratic forms and Northcott property of infinite number fields

General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Quadratic forms over global rings and fields (11E12) Heights (11G50) Algebraic numbers; rings of algebraic integers (11R04) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Other abelian and metabelian extensions (11R20) Totally real fields (11R80)

Cites Work

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On certain infinite extensions of the rationals with Northcott property
Solving the Pell equation
Signature ranks of units in cyclotomic extensions of abelian number fields
Introduction to quadratic forms
Real quadratic fields admitting universal lattices of rank 7
Lifting problem for universal quadratic forms
The unit signature rank deficiency is unbounded over cyclotomic fields
A lower bound for the rank of a universal quadratic form with integer coefficients in a totally real number field
A note on heights in certain infinite extensions of \(\mathbb Q\)
Über die Darstellung total positiver Zahlen des Körpers \(R(\sqrt{5})\) als Summe von drei Quadraten.
Sums of \(m\)th powers of algebraic integers
A note on the Northcott property and undecidability
On the Northcott property and other properties related to polynomial mappings
Definability of the natural numbers in totally real towers of nested square roots
UNIVERSAL QUADRATIC FORMS AND ELEMENTS OF SMALL NORM IN REAL QUADRATIC FIELDS
Über Den Bizyklischen Biquadratischen Zahlkörper
Representations of positive definite quadratic forms.
The 2‐Selmer group of a number field and heuristics for narrow class groups and signature ranks of units
On the Northcott property and local degrees
Redei reciprocity, governing fields and negative Pell
Undecidability, unit groups, and some totally imaginary infinite extensions of ℚ
Undecidability of ℚ⁽²⁾
Julia Robinson numbers
On unit signatures and narrow class groups of odd degree abelian number fields
Northcott numbers for the house and the Weil height
Northcott numbers for the weighted Weil heights
On Kitaoka's conjecture and lifting problem for universal quadratic forms
Definability and decidability for rings of integers in totally imaginary fields
On the Northcott property for infinite extensions
Unit signature ranks in real biquadratic and multiquadratic number fields
Minimal rank of universal lattices and number of indecomposable elements in real multiquadratic fields
Universal quadratic forms and indecomposables in number fields: a survey
Defining \(\mathbb{Z}\) using unit groups

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