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arXiv · 0906.5252

On the Zeta Functions of an optimal tower of function fields over $\FF_4$

Alexey Zaytsev·Gary McGuire
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Abstract

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.

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Alexey Zaytsev, Gary McGuire. 2011-05-23. On the Zeta Functions of an optimal tower of function fields over $\FF_4$. https://arxiv.org/abs/0906.5252

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