TY - JOUR
T1 - Distribution of exponential functions with k-full exponent modulo a prime
AU - Dewar, Michael
AU - Panario, Daniel
AU - Shparlinski, Igor E.
PY - 2004
Y1 - 2004
N2 - For a real x ≥ 1 we denote by Sk[X] the set of k-full integers n ≤ x, that is, the set of positive integers n ≤ x such that ℓk n for any prime divisor ℓ n. We estimate exponential sums of the form T(a, p, x, k) = ∑n∈Sk[x] exp(2πiaθn/p), where θ is a fixed integer with gcd (θ, p) = 1, and apply them to studying the distribution of the powers θn, n ∈ Sk[x], in the residue ring modulo p ≥ 1.
AB - For a real x ≥ 1 we denote by Sk[X] the set of k-full integers n ≤ x, that is, the set of positive integers n ≤ x such that ℓk n for any prime divisor ℓ n. We estimate exponential sums of the form T(a, p, x, k) = ∑n∈Sk[x] exp(2πiaθn/p), where θ is a fixed integer with gcd (θ, p) = 1, and apply them to studying the distribution of the powers θn, n ∈ Sk[x], in the residue ring modulo p ≥ 1.
UR - http://www.scopus.com/inward/record.url?scp=17144427241&partnerID=8YFLogxK
U2 - 10.1016/S0019-3577(04)80014-4
DO - 10.1016/S0019-3577(04)80014-4
M3 - Article
AN - SCOPUS:17144427241
SN - 0019-3577
VL - 15
SP - 497
EP - 503
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 4
ER -