Abstract
We construct an asymptotic formula for a sum function for σ a (α), where σ a (α) is the sum of the ath powers of the norms of divisors of the Gaussian integer α 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 σ a (n) in the form of a series in the Ramanujan sums.
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Sinyavskii, O.V. Sum of Divisors in a Ring of Gaussian Integers. Ukrainian Mathematical Journal 53, 1156–1170 (2001). https://doi.org/10.1023/A:1013333400370
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DOI: https://doi.org/10.1023/A:1013333400370