TY - JOUR

T1 - Distribution of exponential functions with squarefull exponent in residue rings

AU - Shparlinski, Igor E.

PY - 2004/6/21

Y1 - 2004/6/21

N2 - For a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of positive integers n ≤ such that l2 n for any prime divisor l n. We estimate exponential sums of the form Ta (m,x) ∑n∈S[x] exp(2πia vn/m) where ν is a fixed integer with gcd(ν,m) = 1, and apply them to studying the distribution of the powers νn, n ε S[x], in the residue ring modulo m ≥ 1.

AB - For a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of positive integers n ≤ such that l2 n for any prime divisor l n. We estimate exponential sums of the form Ta (m,x) ∑n∈S[x] exp(2πia vn/m) where ν is a fixed integer with gcd(ν,m) = 1, and apply them to studying the distribution of the powers νn, n ε S[x], in the residue ring modulo m ≥ 1.

UR - http://www.scopus.com/inward/record.url?scp=4444260106&partnerID=8YFLogxK

U2 - 10.1016/S0019-3577(04)90020-1

DO - 10.1016/S0019-3577(04)90020-1

M3 - Article

AN - SCOPUS:4444260106

VL - 15

SP - 283

EP - 289

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

SN - 0019-3577

IS - 2

ER -