Let $C$ be a curve of genus $g$.
I heard we can deduce Hasse bound $$ |\sharp C(\mathbb{F}_{q}) - q - 1| \leq 2g\sqrt{q} $$
from congruent zeta function of $C$.
How can we do that?
I only know the case of $g＝1$, elliptic curve case, this is equivalent to Riemann hypothesis of Weil conjecture for elliptic curves. This is equivalent to state that numerator's discriminant is less than $0$.But the same way does not apply to another genus.So I'm stuck.
Thank you in advance.