论文标题
Zhi-hong Sun的四个猜想
Four conjectures by Zhi-Hong Sun
论文作者
论文摘要
我们证明了Zhi-hong Sun对$ \ varepsilon_d^{\ frac {p-1} 4} $的价值$ \ mod p $ p $ p $的猜想，其中$ \ varepsilon_d $是某些领域的norm $ -1 $的单位= \ left（\ frac dp \ right）= 1 $。答案是根据$ p $写入$ p = f（x，y）= u^2+v^2 $，带有$ x，y，u，u，v \ in \ mathbb z $的，其中$ f $是确定性$ -4D $的某些二次形式。
We prove some results conjectured by Zhi-Hong Sun regarding the value $\mod p$ of $\varepsilon_d^{\frac{p-1}4}$, where $\varepsilon_d$ is a unit of norm $-1$ in some fields $\mathbb Q(\sqrt d)$, with $\left(\frac{-1}p\right) =\left(\frac dp\right) =1$. The answer is given in terms of how $p$ writes as $p=f(x,y)=u^2+v^2$, with $x,y,u,v\in\mathbb Z$, where $f$ is a certain quadratic form of determinant $-4d$.
