论文标题
局部可溶性四分之一的方程的积极比例在全球范围内不溶
A positive proportion of locally soluble quartic Thue equations are globally insoluble
论文作者
论文摘要
对于任何固定的非零整数$ h $，我们表明，在本地，在本地代表$ h $的积分二进制四分之一的二进制四分之一的表格$ f $ do do do bug，但在全球范围内不代表$ h $。 我们通过其$ \ textrm {gl} _ {2}（\ Mathbb {z}）$的$ \ textrm {gl} _ {gl} _ {gl {z}）$不变的两个生成器订购了整体二进制四分之一的五分化表单。
For any fixed nonzero integer $h$, we show that a positive proportion of integral binary quartic forms $F$ do locally everywhere represent $h$, but do not globally represent $h$. We order classes of integral binary quartic forms by the two generators of their ring of $\textrm{GL}_{2}(\mathbb{Z})$-invariants, classically denoted by $I$ and $J$.
