(untitled)
Let F_q be a finite field and F_q^s be an extension of F_q. Let f(x)F_q[x] be a polynomial of degree n with gcd(n,q) = 1. We present a recursive formula for evaluating the exponential sum _cF_q^s χ^(s)(f(x)). Let a and b be two elements in F_q with a a≠0, u be a positive integer. We obtain an estimate for the exponential sum _cF^∗_q^s χ^(s) (ac^u+bc^−1), where χ^(s) is the lifting of an additive character χ of F_q. Some properties of the sequences constructed from these exponential sums are provided too. , number=2, journal=Communications in Mathematical Research, year=2022, month=Dec., pages=184–205