TY - JOUR
T1 - Exponential sums over points of elliptic curves with reciprocals of primes
AU - Ostafe, Alina
AU - Shparlinski, Igor E.
N1 - Copyright 2012 University College London. Published by Cambridge University Press. Article originally published in Mathematika, 58(1), pp. 21-33. The original article can be found at http://dx.doi.org/10.1112/S0025579311001719
PY - 2012/1
Y1 - 2012/1
N2 - Abstract 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 g 1/q for an integer g with gcd (g,p)=1 have been estimated by J. Bourgain and I. E. Shparlinski.
AB - Abstract 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 g 1/q for an integer g with gcd (g,p)=1 have been estimated by J. Bourgain and I. E. Shparlinski.
UR - http://www.scopus.com/inward/record.url?scp=84856035442&partnerID=8YFLogxK
U2 - 10.1112/S0025579311001719
DO - 10.1112/S0025579311001719
M3 - Article
AN - SCOPUS:84856035442
VL - 58
SP - 21
EP - 33
JO - Mathematika
JF - Mathematika
SN - 0025-5793
IS - 1
ER -