Zilong He

activity

20132026

k

-universal integral quadratic forms over number fields

6 citations · 14 across the 12 of their papers we have counts for

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Showing 2022Show all

5 papers · 1 filter

math.NT2022★ 2 cited

On classic $n$ -universal quadratic forms over dyadic local fields

Zilong He

Let $n$ be an integer and $n \geq 2$ . A classic integral quadratic form over local fields is called classic $n$ -universal if it represents all $n$ -ary classic integral quadrati…

math.NT2022

Pythagoras number of quartic orders containing $2$

Zilong He, Yong Hu

Let $K$ be a quartic number field containing $2$ and let $O \subseteq K$ be an order such that $2 \in O$ . We prove that the Pythagoras number of $\m…

math.NT2022★ 3 cited

On $k$ -universal quadratic lattices over unramified dyadic local fields

Zilong He, Yong Hu

Let $k$ be a positive integer and let $F$ be a finite unramified extension of $Q_{2}$ with ring of integers $O_{F}$ . An integral (resp. classic) quadratic form over…

math.NT2022★ 2 cited

On $n$ -universal quadratic forms over dyadic local fields

Zilong He, Yong Hu

Let $n \geq 2$ be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be $n$ -universal by using invariants from Bel…

math.NT2022★ 6 cited

On indefinite $k$ -universal integral quadratic forms over number fields

Zilong He, Yong Hu, Fei Xu

An 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 pr…

On classic n-universal quadratic forms over dyadic local fields

Pythagoras number of quartic orders containing 2​

On k-universal quadratic lattices over unramified dyadic local fields

On n-universal quadratic forms over dyadic local fields

On indefinite k-universal integral quadratic forms over number fields

On classic $n$ -universal quadratic forms over dyadic local fields

Pythagoras number of quartic orders containing $2$

On $k$ -universal quadratic lattices over unramified dyadic local fields

On $n$ -universal quadratic forms over dyadic local fields

On indefinite $k$ -universal integral quadratic forms over number fields