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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.16675 |
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| _version_ | 1866914050032533504 |
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| author | Karras, Meselem |
| author_facet | Karras, Meselem |
| contents | Let f be an arithmetic function satisfying certain conditions. In this paper, we give an asymptotic formula for the sum \[\sum_{n_1 n_2 \cdots n_r \leq x} f\left(\left\lfloor \frac{x}{n_1 n_2 \cdots n_r} \right\rfloor\right), \quad r \geq 2.\], where $\lfloor . \rfloor$ denotes the integer part function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hyperbolic summation involving certain arithmetic functions and the integer part function Karras, Meselem Number Theory Let f be an arithmetic function satisfying certain conditions. In this paper, we give an asymptotic formula for the sum \[\sum_{n_1 n_2 \cdots n_r \leq x} f\left(\left\lfloor \frac{x}{n_1 n_2 \cdots n_r} \right\rfloor\right), \quad r \geq 2.\], where $\lfloor . \rfloor$ denotes the integer part function. |
| title | Hyperbolic summation involving certain arithmetic functions and the integer part function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.16675 |