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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2603.16023 |
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| _version_ | 1866912969506422784 |
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| author | Palojärvi, Neea Tudzi, Sebastian |
| author_facet | Palojärvi, Neea Tudzi, Sebastian |
| contents | In this article, we obtain effective estimates for the error term $Δ_{k}(x)$ for all integers $k \geq2$, and completely explicit estimates for integers $k \in [3,9]$. The explicit results improve the powers of $x$ appearing in the known explicit bounds for $Δ_{k}(x)$, and the effective bounds provide a method to derive such bounds for all integers $k\geq 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16023 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Explicit and Effective Estimates for the error term in the Generalised Divisor Problem Palojärvi, Neea Tudzi, Sebastian Number Theory 11N99 In this article, we obtain effective estimates for the error term $Δ_{k}(x)$ for all integers $k \geq2$, and completely explicit estimates for integers $k \in [3,9]$. The explicit results improve the powers of $x$ appearing in the known explicit bounds for $Δ_{k}(x)$, and the effective bounds provide a method to derive such bounds for all integers $k\geq 3$. |
| title | Explicit and Effective Estimates for the error term in the Generalised Divisor Problem |
| topic | Number Theory 11N99 |
| url | https://arxiv.org/abs/2603.16023 |