Resumen de Counting points on hyperelliptic curves in average polynomial time

David Harvey

• Let g=1 , and let Q?Z[x] be a monic, squarefree polynomial of degree 2g+1 . For an odd prime p not dividing the discriminant of Q , let Z p (T) denote the zeta function of the hyperelliptic curve of genus g over the finite field F p obtained by reducing the coefficients of the equation y 2 =Q(x) modulo p . We present an explicit deterministic algorithm that given as input Q and a positive integer N , computes Z p (T) simultaneously for all such primes p