Exponential Sums over Points of Elliptic Curves with Reciprocals of Primes
نویسندگان
چکیده
We consider exponential sums with x-coordinates of points qG and q−1G where G is a point of order T on an elliptic curve modulo a prime p and q runs through all primes up to N (with gcd(q, T )= 1 in the case of the points q−1G). We obtain a new bound on exponential sums with q−1G and correct an imprecision in the work of W. D. Banks, J. B. Friedlander, M. Z. Garaev and I. E. Shparlinski on exponential sums with qG. We also note that similar sums with g1/q for an integer g with gcd(g, p)= 1 have been estimated by J. Bourgain and I. E. Shparlinski. §
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