Sums of the higher divisor function of diagonal homogeneous forms in short intervals
Let $ d_k(n) $ denote the k-th divisor function. In this paper, we give the asymptotic formula of the sum $ \sum\limits_{\substack{x-y\le n_i^r \le x+y \\ i = 1,2,\ldots,l} }{d_k(n_1^r+n_2^r+\ldots+n_l^r)}, $ where $ n_1, n_2, \ldots, n_l \in \mathbb{Z}^+ $, $ k\ge2 $, $ r\ge 3 $ and $ l &a...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-07-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231150?viewType=HTML |