A weighted divisor problem and exponential sum
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913923127574528 |
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| author | Aggarwal, Kritika Banerjee, Debika |
| author_facet | Aggarwal, Kritika Banerjee, Debika |
| contents | In this paper, we investigate a weighted divisor problem involving the exponential sum of $D_{(1)}(n)$, the $n$th coefficient in the Dirichlet series expansion of $ζ'(s)^2$. We establish a truncated Voronoï type formula for the error term of $\sum_{n\leq x}D_{(1)}(n)e(nh/k)$, analogous to the results obtained by Jutila. Utilizing this truncated formula, we derive a mean square estimate of the error term. In addition, we study the associated Riesz sum and the corresponding error term, along with its mean square estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A weighted divisor problem and exponential sum Aggarwal, Kritika Banerjee, Debika Number Theory 11N37, 11L07, 11M06 (Primary) 33C10 (Secondary) In this paper, we investigate a weighted divisor problem involving the exponential sum of $D_{(1)}(n)$, the $n$th coefficient in the Dirichlet series expansion of $ζ'(s)^2$. We establish a truncated Voronoï type formula for the error term of $\sum_{n\leq x}D_{(1)}(n)e(nh/k)$, analogous to the results obtained by Jutila. Utilizing this truncated formula, we derive a mean square estimate of the error term. In addition, we study the associated Riesz sum and the corresponding error term, along with its mean square estimate. |
| title | A weighted divisor problem and exponential sum |
| topic | Number Theory 11N37, 11L07, 11M06 (Primary) 33C10 (Secondary) |
| url | https://arxiv.org/abs/2507.01891 |