Riemann Hypothesis for Goss $t$-adic Zeta Function

Javier Diaz-Vargas, Enrique Polanco-Chi

In this short note, we give a proof of the Riemann hypothesis for Goss $v$-adic zeta function ${\zeta }_v(s)$, when $v$ is a prime of ${\mathbb{F}}_q[t]$ of degree one.