Norm of Gaussian integers in arithmetical progressions and narrow sectors

• Veröffentlicht in: Algebra and Discrete Mathematics
• Datum: 2020
• Hauptverfasser: Varbanets, S., Vorobyov, Y.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут прикладної математики і механіки НАН України 2020
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/188520
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.