Sum of divisors in a ring of gaussian integers

We construct an asymptotic formula for a sum function for σa(α), where σa(α) is the sum of the ath powers of the norms of divisors of the Gaussian integer a on an arithmetic progression α = α0 (mod γ) and in a narrow sector (φ1 ≤ arg α < φ2- For this purpose, we use a representation of σa(n) in the form of a series in the Ramanujan sums. © 2001 Plenum Publishing Corporation.