Abstract
Let 𝔽q be a finite field with q = pe 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 2F1 hypergeometric functions. Also, we find some identities, and particular values of hypergeometric functions over 𝔽q.
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