Sum of Divisors in a Ring of Gaussian Integers

• Date: 2001
• Main Authors: Sinyavskii, O. V., Синявский, О. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4317
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...