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Sums of higher divisor functions
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-03-01 , DOI: 10.1016/j.jnt.2020.08.009
Guangwei Hu , Guangshi Lü

Abstract Let d k ( n ) denote the k-th divisor function. In this paper, we study the asymptotic formula of the sum ∑ 1 ≤ n 1 , n 2 , … , n l ≤ x d k ( n 1 2 + n 2 2 + ⋯ + n l 2 ) , where n 1 , n 2 , … , n l ∈ Z + , k ≥ 4 and l ≥ 3 are integers. Previously only the cases of k = 2 , 3 are studied.

中文翻译:

高除数函数的总和

摘要 令 dk ( n ) 表示第 k 个除数函数。在本文中,我们研究和 ∑ 1 ≤ n 1 , n 2 , … , nl ≤ xdk ( n 1 2 + n 2 2 + ⋯ + nl 2 ) 的渐近公式,其中 n 1 , n 2 , … , nl ∈ Z + ,k ≥ 4 和 l ≥ 3 是整数。以前只研究了 k = 2 , 3 的情况。
更新日期:2021-03-01
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