Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.11069 |
| Tags: |
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Sommario:
- Let $Δ_{k}(x)$ be the error term in the classical asymptotic formula for the sum $\sum_{n\leq x}d_{k}(n)$, where $d_{k}(n)$ is the number of ways $n$ can be written as a product of $k$ factors. We study the analytic properties of the Dirichlet series $\sum_{n=1}^{\infty}Δ_{k}(n)n^{-s}$ and use Perron's formula to estimate the sums $\sum_{n\leq x}Δ_{3}(n)$ and $\sum_{n\leq x}Δ_{4}(n)$ for large $x>0$.