Hyperelliptic Curves and its Applications

摘要

Let Fq be a finite field with q= p~e elements, where p is a prime. We calculate the number of zeros of the hyperelliptic curve by using the properties of the quadratic character. With the help of these zeros we discuss the trace of Frobenius map on the hyperelliptic curves in terms of special values of _2F_1 hypergeometric functions. Also, we find some identities, and particular values of hypergeometric functions over F_q.