Sum of divisors in a ring of gaussian integers

被引：0

作者：

Sinyavskii O.V. ^{[1
]}

机构：

[1] Odessa University, Odessa

来源：

Ukrainian Mathematical Journal | 2001年 / 53卷 / 7期

关键词：

Asymptotic Formula; Arithmetic Progression; Narrow Sector; Gaussian Integer;

D O I：

10.1023/A:1013333400370

中图分类号：

学科分类号：

摘要：

We construct an asymptotic formula for a sum function for σa(α), where σa(α) is the sum of the ath powers of the norms of divisors of the Gaussian integer a 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 σa(n) in the form of a series in the Ramanujan sums. © 2001 Plenum Publishing Corporation.

引用

页码：1156 / 1170

页数：14

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