Sum of Divisors in a Ring of Gaussian Integers

  • O. V. Sinyavskii


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 (n) in the form of a series in the Ramanujan sums.
How to Cite
Sinyavskii, O. V. “Sum of Divisors in a Ring of Gaussian Integers”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 53, no. 7, July 2001, pp. 970-82,
Research articles