Computing zeta functions for ordinary formal groups over finite fields Original Research Article

We describe an algorithm to compute the one-dimensional part of the zeta function ZG of an ordinary formal group law G of finite dimension d over a finite field of pN elements and evaluate its time computational complexity. Assume G is given as d formal power series in 2d variables. Our algorithm computes ZG mod pt with O(d2p(t−1)(2d+3)N2(log p)2) bit operations.