Exponential sums over points of elliptic curves with reciprocals of primes

Alina Ostafe*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
7 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)21-33
Number of pages13
Issue number1
Publication statusPublished - Jan 2012

Bibliographical note

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


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