A segment of Euler product associated to a certain Dirichlet series
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917812583268352 |
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| author | Gupta, Rajat Savalia, Aditi |
| author_facet | Gupta, Rajat Savalia, Aditi |
| contents | In the spirit of the work of Hardy-Littlewood and Lavrik, we study the Dirichlet series associated to the generalized divisor function $σ_α(n):=\sum_{d|n}d^α$. We obtain an exact identity relating the Dirichlet series $ζ(s)ζ(s-α)$ and a segment of the Euler product attached to it. Specifically, our main theorems are valid in the critical strip. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16940 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A segment of Euler product associated to a certain Dirichlet series Gupta, Rajat Savalia, Aditi Number Theory Primary 11M41, Secondary, 11M06 In the spirit of the work of Hardy-Littlewood and Lavrik, we study the Dirichlet series associated to the generalized divisor function $σ_α(n):=\sum_{d|n}d^α$. We obtain an exact identity relating the Dirichlet series $ζ(s)ζ(s-α)$ and a segment of the Euler product attached to it. Specifically, our main theorems are valid in the critical strip. |
| title | A segment of Euler product associated to a certain Dirichlet series |
| topic | Number Theory Primary 11M41, Secondary, 11M06 |
| url | https://arxiv.org/abs/2410.16940 |