Add to ORKGAn integral quadratic lattice is called indefinite $k$-universal if it represents all integral quadratic lattices of rank $k$ for a given positive integer $k$. For $k\geq 3$, we prove that the indefinite $k$-universal property satisfies the local-global principle over number fields. For $k=2$, we show that a number field $F$ admits an integral quadratic lattice which is locally $2$-universal but not indefinite 2-universal if and only if the class number of $F$ is even. Moreover, there are only finitely many classes of such lattices over $F$. For $k=1$, we prove that $F$ admits a classic integral lattice which is locally classic $1$-universal but not classic indefinite $1$-universal if and only if $F$ has a quadratic unramified extensi...
We prove the failure of the local-global principle, with respect to discrete valuations, for isotrop...
The aim of this work is to study universal quadratic forms over biquadratic fields. In the thesis we...
EnKim, Kim, and Oh gave a minimal criterion for the 2-universality of positivedefinite integer-matri...
Let $k$ be a positive integer and let $F$ be a finite unramified extension of $\mathbb{Q}_2$ with ri...
We give an overview of universal quadratic forms and lattices, focusing onthe recent developments ov...
The Fifteen Theorem deals with universal integral quadratic form. In 1770 Lagrange proved that the q...
Let $ n $ be an integer and $ n\ge 2 $. We determine the equivalent conditions and establish a local...
For a quadratic form over a totally real number field $K$, we show that there are only finitely many...
We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadr...
We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fiel...
Abstract. The purpose of this paper is to announce several results describing properties of the almo...
AbstractLet (F, p) be a quadratic ramified extension of the field Q2 of 2-adic numbers, with D its r...
AbstractH. Pfeuffer [J. Number Theory 11 (1979), 188–196] showed that totally positive quadratic for...
We show that if a universal quadratic form exists over an infinite degree, totally real extension of...
Let $\mathfrak o$ be the ring of integers of a totally real number field. If $f$ is a quadratic form...
We prove the failure of the local-global principle, with respect to discrete valuations, for isotrop...
The aim of this work is to study universal quadratic forms over biquadratic fields. In the thesis we...
EnKim, Kim, and Oh gave a minimal criterion for the 2-universality of positivedefinite integer-matri...
Let $k$ be a positive integer and let $F$ be a finite unramified extension of $\mathbb{Q}_2$ with ri...
We give an overview of universal quadratic forms and lattices, focusing onthe recent developments ov...
The Fifteen Theorem deals with universal integral quadratic form. In 1770 Lagrange proved that the q...
Let $ n $ be an integer and $ n\ge 2 $. We determine the equivalent conditions and establish a local...
For a quadratic form over a totally real number field $K$, we show that there are only finitely many...
We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadr...
We prove that in each degree divisible by 2 or 3, there are infinitely many totally real number fiel...
Abstract. The purpose of this paper is to announce several results describing properties of the almo...
AbstractLet (F, p) be a quadratic ramified extension of the field Q2 of 2-adic numbers, with D its r...
AbstractH. Pfeuffer [J. Number Theory 11 (1979), 188–196] showed that totally positive quadratic for...
We show that if a universal quadratic form exists over an infinite degree, totally real extension of...
Let $\mathfrak o$ be the ring of integers of a totally real number field. If $f$ is a quadratic form...
We prove the failure of the local-global principle, with respect to discrete valuations, for isotrop...
The aim of this work is to study universal quadratic forms over biquadratic fields. In the thesis we...
EnKim, Kim, and Oh gave a minimal criterion for the 2-universality of positivedefinite integer-matri...