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 -