论文标题
对角线形式的Hasse原理仅限于较低的高度曲面
The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces
论文作者
论文摘要
我们建立了由一种对角线形式的$ k $和一种$ d $的一般形式的对角形式组成的双对角系统的分析哈斯原理，其中$ d $小于$ k $。通过采用一种混合方法，将一般形式的研究中的思想与适合对角线情况的技术结合在一起，我们能够获得在$ d $中呈指数增长的界限，但仅在$ k $中占四倍，反映出通常分别针对这两个问题获得的增长率。我们还讨论了我们方法中最有趣的概括。
We establish the analytic Hasse principle for Diophantine systems consisting of one diagonal form of degree $k$ and one general form of degree $d$, where $d$ is smaller than $k$. By employing a hybrid method that combines ideas from the study of general forms with techniques adapted to the diagonal case, we are able to obtain bounds that grow exponentially in $d$ but only quadratically in $k$, reflecting the growth rates typically obtained for both problems separately. We also discuss some of the most interesting generalisations of our approach.
