A Pfaffian Proof and Generalization of a Conjecture of Sun Zhiwei

Hong-Ge Chen, Fei Liu

Let $p$ be an odd prime, let $n=(p-1)/2$, and let $\ddot{I}‡=(\frac{\cdot }{p})$, with $\ddot{I}‡(0)=0$. For $a\in {\mathbb{F}}_p^{\times }$ define \[ D_a(x)=\det_{1\le i,j\le n}(x+χ(i^2-aj)), \qquad D…