TY - JOUR
T1 - Exponential sums with consecutive modular roots of an integer
AU - Shparlinski, Igor E.
PY - 2011/3
Y1 - 2011/3
N2 - J. Bourgain and the author have recently estimated exponential sums with consecutive modular roots θ1/n (mod p), where θ is of multiplicative order t ≥ pε modulo a prime p (for some fixed ε > 0) and n runs through the integers in the interval [M + 1, M + N] with gcd(n, t) = 1. However, the saving in that bound against the trivial estimate has not been made explicit. It is shown here that for t ≥ p 1/2+ε one can obtain a fully explicit bound for such exponential sums.
AB - J. Bourgain and the author have recently estimated exponential sums with consecutive modular roots θ1/n (mod p), where θ is of multiplicative order t ≥ pε modulo a prime p (for some fixed ε > 0) and n runs through the integers in the interval [M + 1, M + N] with gcd(n, t) = 1. However, the saving in that bound against the trivial estimate has not been made explicit. It is shown here that for t ≥ p 1/2+ε one can obtain a fully explicit bound for such exponential sums.
UR - http://www.scopus.com/inward/record.url?scp=79951868905&partnerID=8YFLogxK
U2 - 10.1093/qmath/hap023
DO - 10.1093/qmath/hap023
M3 - Article
AN - SCOPUS:79951868905
SN - 0033-5606
VL - 62
SP - 207
EP - 213
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 1
ER -