Abstract
In the present paper, the distribution of pseudorandom vectors, derived from a specific set of rational points on elliptic curves over finite fields, is studied by estimating its discrepancy based on the system of Walsh functions and exponential sums over elliptic curves. It turns out these pseudorandom vectors have good behaviors, such as uniform distribution and strong pseudorandomness. Moreover, we apply the incomplete sum to the elliptic curve version of sum-product and Sárközy problems.
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