TY - JOUR
T1 - Bilinear sums with exponential functions
AU - Shparlinski, Igor E.
N1 - Copyright 2009 American Mathematical Society. First published in Proceedings of the American Mathematical Society, Volume 137, Issue 7, pp. 2217-2224, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0002-9939-09-09882-7.
PY - 2009/7
Y1 - 2009/7
N2 - Let g ≠0,±1 be a fixed integer. Given two sequences of complex numbers (ζm)∞
m=1 and (ψn) ∞
n=1 and two sufficiently large integers M and N, we estimate the exponential sums ∑/p≥M/gcd(ag,p)=1 ∑/1≥n≥N ζpψnep(agn), a ∈ ℤ, where the outer summation is taken over all primes p ≥ M with gcd(ag, p) = 1.
AB - Let g ≠0,±1 be a fixed integer. Given two sequences of complex numbers (ζm)∞
m=1 and (ψn) ∞
n=1 and two sufficiently large integers M and N, we estimate the exponential sums ∑/p≥M/gcd(ag,p)=1 ∑/1≥n≥N ζpψnep(agn), a ∈ ℤ, where the outer summation is taken over all primes p ≥ M with gcd(ag, p) = 1.
UR - http://www.scopus.com/inward/record.url?scp=77951047758&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-09-09882-7
DO - 10.1090/S0002-9939-09-09882-7
M3 - Article
AN - SCOPUS:77951047758
SN - 0002-9939
VL - 137
SP - 2217
EP - 2224
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 7
ER -