Computing Zeta Functions of Hyperelliptic Curves over Finite Fields of Characteristic 2

摘要

We present an algorithm for computing the zeta function of an arbitrary hyperelliptic curve over a finite field F_q of characteristic 2, thereby extending the algorithm of Kedlaya for small odd characteristic. For a genus g hyperelliptic curve over F_(2~n), the asymptotic running time of the algorithm is O(g~(5+ε)n~(3+ε)) and the space complexity is O(g~3n~3).