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 -