We give an overview of universal quadratic forms and lattices, focusing onthe recent developments over the rings of integers in totally real numberfields. In particular, we discuss indecomposable algebraic integers as one ofthe main tools.Comment: 34 pages, journal versio
Recent ground-breaking work of Conway, Schneeberger, Bhargava, and Hanke shows that to determine whe...
We show that the ring of integers of $\mathbb{Q}^{\text{tr}}$ is existentially definable in the ring...
A number of recent results give constructions of totally real number fields of specific degrees that...
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fiel...
The aim of this work is to study universal quadratic forms over biquadratic fields. In the thesis we...
The aim of this work is to study the number of variables of universal quadratic forms in number fiel...
An integral quadratic lattice is called indefinite $k$-universal if it represents all integral quadr...
We show that if a universal quadratic form exists over an infinite degree, totally real extension of...
We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadr...
For a quadratic form over a totally real number field $K$, we show that there are only finitely many...
AbstractH. Pfeuffer [J. Number Theory 11 (1979), 188–196] showed that totally positive quadratic for...
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
A number of recent results give constructions of totally real number fields of specific degrees that...
Let $k$ be a positive integer and let $F$ be a finite unramified extension of $\mathbb{Q}_2$ with ri...
Recent ground-breaking work of Conway, Schneeberger, Bhargava, and Hanke shows that to determine whe...
We show that the ring of integers of $\mathbb{Q}^{\text{tr}}$ is existentially definable in the ring...
A number of recent results give constructions of totally real number fields of specific degrees that...
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fiel...
The aim of this work is to study universal quadratic forms over biquadratic fields. In the thesis we...
The aim of this work is to study the number of variables of universal quadratic forms in number fiel...
An integral quadratic lattice is called indefinite $k$-universal if it represents all integral quadr...
We show that if a universal quadratic form exists over an infinite degree, totally real extension of...
We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadr...
For a quadratic form over a totally real number field $K$, we show that there are only finitely many...
AbstractH. Pfeuffer [J. Number Theory 11 (1979), 188–196] showed that totally positive quadratic for...
This thesis focuses on additively indecomposable integers in totally real number fields and their ap...
A number of recent results give constructions of totally real number fields of specific degrees that...
Let $k$ be a positive integer and let $F$ be a finite unramified extension of $\mathbb{Q}_2$ with ri...
Recent ground-breaking work of Conway, Schneeberger, Bhargava, and Hanke shows that to determine whe...
We show that the ring of integers of $\mathbb{Q}^{\text{tr}}$ is existentially definable in the ring...
A number of recent results give constructions of totally real number fields of specific degrees that...
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