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 -