Denote $\Theta_C$ as the Frobenius class of a curve $C$ over the finite field$\mathbb{F}_q$. In this paper we determine the expected value ofTr$(\Theta_C^n)$ where $C$ runs over all biquadratic curves when $q$ is fixedand $g$ tends to infinity. This extends work done by Rudnick and Chinis whoseparately looked at hyperelliptic curves and Bucur, Costa, David, Guerreiroand Lowry-Duda who looked at $\ell$-cyclic curves, for $\ell$ a prime, as wellas cubic non-Galois curves.
展开▼
机译：将$ \ Theta_C $表示为有限域$ \ mathbb {F} _q $上曲线$ C $的Frobenius类。在本文中，我们确定Tr $（\ Theta_C ^ n）$的期望值，其中当$ q $固定且$ g $趋于无穷大时，$ C $遍历所有双二次曲线。这扩展了Rudnick和Chinis分别研究超椭圆曲线的工作以及Bucur，Costa，David，Guerreiro和Lowry-Duda的工作，他们研究了$ \ ell $循环曲线，质数$ \ ell $以及三次非加洛伊斯曲线。
展开▼
