Premium
EXPONENTIAL SUMS OVER POINTS OF ELLIPTIC CURVES WITH RECIPROCALS OF PRIMES
Author(s) -
Ostafe Alina,
Shparlinski Igor E.
Publication year - 2012
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579311001719
Subject(s) - mathematics , exponential function , modulo , integer (computer science) , elliptic curve , order (exchange) , combinatorics , prime (order theory) , exponential sum , discrete mathematics , pure mathematics , mathematical analysis , finance , computer science , economics , programming language
We consider exponential sums with x ‐coordinates of points qG and q −1 G 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 −1 G ). We obtain a new bound on exponential sums with q −1 G 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.