We first study the mean value of certain restricted divisor sums involving the Chowla–Walum sums, improving in particular a recent estimate given by Iannucci. The aim of the second part of this work is the generalization of the previous study, by restricting the range of the divisors in the studied divisor sums, extending the Chowla–Walum conjecture, proving a small part of this extended conjecture and generalizing the asymptotic formulas previously obtained in the first part.

中文翻译：

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关于与 Chowla-Walum 猜想相关的受限除数

我们首先研究了涉及 Chowla-Walum 和的某些受限除数和的平均值，特别是改进了 Iannucci 最近给出的估计。这项工作的第二部分的目的是对先前研究的推广，通过限制所研究的因数和中的因数范围，扩展 Chowla-Walum 猜想，证明这个扩展猜想的一小部分并推广渐近公式之前在第一部分中获得。