论文标题
$ \ mathbb {q} _2 $的添加形式两次添加形式的溶解度两次奇数。
Solubility of Additive Forms of Twice Odd Degree over Ramified Quadratic Extensions of $\mathbb{Q}_2$
论文作者
论文摘要
我们确定变量的最小数量$γ^*（d，k）$，保证每种添加剂的$ d = 2m $，$ m $ odd，$ m \ ge 3 $的添加剂解决方案，$ \ mathbb {q} _2 $。我们证明，如果$ k $是$ \ {\ mathbb {q} _2（\ sqrt {2}），\ mathbb {q} _2（\ sqrt {10}}），\ \ mathbb {q} \ Mathbb {q} _2（\ sqrt {-10}）\} $，$γ^*（d，d，k）= \ frac {3} {2} d $，如果$ k $是$ \ \ \ \ \ \ \ {\ MathBB {Q} _2（Q} _2（ \ Mathbb {q} _2（\ sqrt {-5}）\} $，$γ^*（d，k）= d+1 $。案例$ d = 6 $以前是众所周知的。
We determine the minimal number of variables $Γ^*(d, K)$ which guarantees a nontrivial solution for every additive form of degree $d=2m$, $m$ odd, $m \ge 3$ over the six ramified quadratic extensions of $\mathbb{Q}_2$. We prove that if $K$ is one of $\{\mathbb{Q}_2(\sqrt{2}), \mathbb{Q}_2(\sqrt{10}), \mathbb{Q}_2(\sqrt{-2}), \mathbb{Q}_2(\sqrt{-10})\}$, $Γ^*(d,K) = \frac{3}{2}d$, and if $K$ is one of $\{\mathbb{Q}_2(\sqrt{-1}), \mathbb{Q}_2(\sqrt{-5})\}$, $Γ^*(d,K) = d+1$. The case $d=6$ was previously known.
