TY - JOUR

T1 - Congruences and exponential sums with the sum of aliquot divisors function

AU - Balasuriya, Sanka

AU - Banks, William D.

AU - Shparlinski, Igor E.

PY - 2008

Y1 - 2008

N2 - We give bounds on the number of integers 1 ≤ n ≤ N such that p s(n), where p is a prime and s(n) is the sum of aliquot divisors function given by s(n) = σ(n) - n, where - (n) is the sum of divisors function. Using this result, we obtain nontrivial bounds in certain ranges for rational exponential sums of the form Sp (a,N) = ∑n≤N exp(2πias(n)/p), gcd(a,p) = 1.

AB - We give bounds on the number of integers 1 ≤ n ≤ N such that p s(n), where p is a prime and s(n) is the sum of aliquot divisors function given by s(n) = σ(n) - n, where - (n) is the sum of divisors function. Using this result, we obtain nontrivial bounds in certain ranges for rational exponential sums of the form Sp (a,N) = ∑n≤N exp(2πias(n)/p), gcd(a,p) = 1.

UR - http://www.scopus.com/inward/record.url?scp=58249087187&partnerID=8YFLogxK

U2 - 10.1142/S179304210800178X

DO - 10.1142/S179304210800178X

M3 - Article

AN - SCOPUS:58249087187

VL - 4

SP - 903

EP - 909

JO - International Journal of Number Theory

JF - International Journal of Number Theory

SN - 1793-0421

IS - 6

ER -