A bootstrap for the number of ${\mathbb{F}}_{q^r}$-rational points on a curve over ${\mathbb{F}}_q$

Santiago Molina, Narcís Sayols, Sebastià Xambó-Descamps

In this note we present a fast algorithm that finds for any $r$ the number $N_r$ of ${\mathbb{F}}_{q^r}$ rational points on a smooth absolutely irreducible curve $C$ defined over $\m…