What is the form of zeta function of an elliptic curve over $\mathbb{F}\_p(t)$? Does it satisfy a Riemann hypothesis?



Zeta function of an elliptic curve over $\mathbb{F}_p(t)$
It is a polynomial in $p^{-s}$ and yes, it satisfies the Riemann hypothesis. See for example Theorem 2.2.1 of Lecture 4 of Douglas Ulmer's *Elliptic curves over function fields* available on the arXiv: [1101.1939v1](http://arxiv.org/abs/1101.1939v1).


