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

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

2009-06-29

arxiv.org/abs/0906.5252v3

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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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