On the Mean Value of a Weighted Composite Arithmetic Function
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918352565305344 |
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| author | Bouderbala, Mihoub |
| author_facet | Bouderbala, Mihoub |
| contents | The primary objective of this paper is to employ methods from analytic number theory to investigate the mean value properties of a composite function involving the Dirichlet divisor function and a generalized minimal power function. Specifically, we study the weighted summatory function where the divisor function is normalized by the number of distinct prime factors. We establish a rigorous asymptotic formula for this sum, detailing the analytic properties of the associated Dirichlet series and the contour integration process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_16027 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Mean Value of a Weighted Composite Arithmetic Function Bouderbala, Mihoub Number Theory 11A25, 11N37, 11M06 The primary objective of this paper is to employ methods from analytic number theory to investigate the mean value properties of a composite function involving the Dirichlet divisor function and a generalized minimal power function. Specifically, we study the weighted summatory function where the divisor function is normalized by the number of distinct prime factors. We establish a rigorous asymptotic formula for this sum, detailing the analytic properties of the associated Dirichlet series and the contour integration process. |
| title | On the Mean Value of a Weighted Composite Arithmetic Function |
| topic | Number Theory 11A25, 11N37, 11M06 |
| url | https://arxiv.org/abs/2602.16027 |