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arXiv · 1707.06531

Expected Value of High Powers of Trace of Frobenius of Biquadratic Curves Over a Finite Field

Patrick Meisner
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Abstract

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 of Tr$(\Theta_C^n)$ where $C$ runs over all biquadratic curves when $q$ is fixed and $g$ tends to infinity. This extends work done by Rudnick and Chinis who separately looked at hyperelliptic curves and Bucur, Costa, David, Guerreiro and Lowry-Duda who looked at $\ell$-cyclic curves, for $\ell$ a prime, as well as cubic non-Galois curves.

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Patrick Meisner. 2017-07-20. Expected Value of High Powers of Trace of Frobenius of Biquadratic Curves Over a Finite Field. https://arxiv.org/abs/1707.06531

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