Norm of Gaussian integers in arithmetical progressions and narrow sectors - Varbanets, S.; Vorobyov, Y. (Algebra and Discrete Mathematics, 2020)
We proved the equidistribution of the Gaussian integer numbers in narrow sectors of the circle of radius x¹/² , x → ∞, with the norms belonging to arithmetic progression N(α) ≡ ℓ (mod q) with the common difference of an arithmetic progression q, q ≪ x²/³⁻ᵋ.