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 -