Norm of Gaussian integers in arithmetical progressions and narrow sectors

• Published in: Algebra and Discrete Mathematics
• Date: 2020
• Main Authors: Varbanets, S., Vorobyov, Y.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2020
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/188520
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Norm of Gaussian integers in arithmetical progressions and narrow sectors / S. Varbanets, Y. Vorobyov // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 2. — С. 259–270. — Бібліогр.: 4 назв. — англ.

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.