TY - JOUR
T1 - Character sums with exponential functions over smooth numbers
AU - Banks, William D.
AU - Friedlander, John B.
AU - Garaev, Moubariz Z.
AU - Shparlinski, Igor E.
PY - 2006/6/19
Y1 - 2006/6/19
N2 - We give nontrivial bounds in various ranges for exponential sums of the formunder(∑, n ∈ S (x, y)) exp (2 π i a θ{symbol}n / m) and under(∑, n ∈ St (x, y)) exp (2 π i a θ{symbol}n / m)where m ≥ 2, φ is an element of order t in the multiplicative group Z*m, gcd(a,m) = 1, S(x,y) is the set of y-smooth integers n≤x, and St(x,y) is the subset of S(x,y) consisting of integers that are coprime to t. We obtain sharper bounds in the special case that m = q is a prime number.
AB - We give nontrivial bounds in various ranges for exponential sums of the formunder(∑, n ∈ S (x, y)) exp (2 π i a θ{symbol}n / m) and under(∑, n ∈ St (x, y)) exp (2 π i a θ{symbol}n / m)where m ≥ 2, φ is an element of order t in the multiplicative group Z*m, gcd(a,m) = 1, S(x,y) is the set of y-smooth integers n≤x, and St(x,y) is the subset of S(x,y) consisting of integers that are coprime to t. We obtain sharper bounds in the special case that m = q is a prime number.
UR - http://www.scopus.com/inward/record.url?scp=33746887463&partnerID=8YFLogxK
U2 - 10.1061/(ASCE)0733-9372(2006)132:2(157)
DO - 10.1061/(ASCE)0733-9372(2006)132:2(157)
M3 - Article
AN - SCOPUS:33746887463
SN - 0019-3577
VL - 17
SP - 157
EP - 168
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 2
ER -