TY - JOUR
T1 - Exponential and character sums with mersenne numbers
AU - Banks, William D.
AU - Friedlander, John B.
AU - Garaev, Moubariz Z.
AU - Shparlinski, Igor E.
PY - 2012/2
Y1 - 2012/2
N2 - We give new bounds on sums of the form Σ n≤N ∧ (n) exp (2πiag n/m) and Σ n≤N ∧ (n)Χ(g n + a), where ∧ is the von Mangoldt function, m is a natural number, a and g are integers coprime to m, and Χ is a multiplicative character modulom. In particular, our results yield bounds on the sums Σ p≤N exp (2πiaM p/m) and Σ p≤N Χ(M p) with Mersenne numbers M p = 2 p - 1, where p is prime.
AB - We give new bounds on sums of the form Σ n≤N ∧ (n) exp (2πiag n/m) and Σ n≤N ∧ (n)Χ(g n + a), where ∧ is the von Mangoldt function, m is a natural number, a and g are integers coprime to m, and Χ is a multiplicative character modulom. In particular, our results yield bounds on the sums Σ p≤N exp (2πiaM p/m) and Σ p≤N Χ(M p) with Mersenne numbers M p = 2 p - 1, where p is prime.
UR - http://www.scopus.com/inward/record.url?scp=84862532380&partnerID=8YFLogxK
U2 - 10.1017/S1446788712000109
DO - 10.1017/S1446788712000109
M3 - Article
AN - SCOPUS:84862532380
VL - 92
SP - 1
EP - 13
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
SN - 1446-7887
IS - 1
ER -