Sum of Divisors in a Ring of Gaussian Integers

We construct an asymptotic formula for a sum function for _a(), where _a() is the sum of the ath powers of the norms of divisors of the Gaussian integer on an arithmetic progression ₀ (mod ) and in a narrow sector ₁ arg < ₂. For this purpose, we use a representation of _a(n) in the form of a series in the Ramanujan sums.