Geodesic
An additive divisor problem in Z[i]
Algebra and discrete mathematics, no. 1 (2003), pp. 103-110.

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Let τ(α) be the number of divisors of the Gaussian integer α. An asymptotic formula for the summatory function ∑N(α)≤xτ(α)τ(α+β) is obtained under the condition N(β)≤x3/8. This is a generalization of the well-known additive divisor problem for the natural numbers.
Mots-clés : additive divisor problem; asymptotic formula. 
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O. V. Savasrtu; P. D. Varbanets. An additive divisor problem in $\mathbb{Z}[i]$. Algebra and discrete mathematics, no. 1 (2003), pp. 103-110. https://geodesic-test.mathdoc.fr/item/ADM_2003_1_a9/