# 电竞菠菜外围app

Universal quadratic forms over number fields

Let $k$ be a positive integer and let $f=f(x_1,\ldots, x_n)$ be an integral quadratic form. We say that $f$ is $k$-universal if for every integral quadratic form $g=g(y_1,\ldots,y_k)$ in $k$ variables, there exist linear forms with integral coefficients $l_1(y_1, \ldots,y_k), \ldots, l_m(y_1, \ldots, y_k)$ such that $f(l_1, \ldots,l_m)=g$. In this talk, I will report some recent progress on the classification of $k$-universal quadratic forms over $p$-adic fields and number fields. This is based on joint works with He Zilong and Xu Fei.