On the Zeta Functions of an optimal tower of function fields over $\FF_4$
Alexey Zaytsev, Gary McGuire · arXiv (Cornell University) · 2009
In this paper we derive a recursion for the zeta function of each function field in the second Garcia-Stichtenoth tower when $q=2$. We obtain our recursion by applying a theorem of Kani and Rosen that gives information about the decomposition of the Jacobians. This enables us to compute the zeta functions explicitly of the first six function fields.