Jordan S. Ellenberg

Nonvanishing of hyperelliptic zeta functions over finite fields

2020 · Algebra & Number Theory

Fixing $t \in \mathbb{R}$ and a finite field $\mathbb{F}_q$ of odd characteristic, we give an explicit upper bound on the proportion of genus $g$ hyperelliptic curves over $\mathbb{F}_q$ whose zeta function vanishes at $\frac{1}{2} + …