Computing zeta functions of arithmetic schemes

We present new algorithms for computing zeta functions of algebraic varieties over finite fields. In particular, let X be an arithmetic scheme (scheme of finite type over Z ), and for a prime p let ζXp(s) be the local factor of its zeta function. We present an algorithm that computes ζXp(s) for a single prime p in time p1/2+o(1) , and another algorithm that computes ζXp(s) for all primes p

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