Mean values of long Dirichlet polynomials with divisor coefficients
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915347167182848 |
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| author | Cicek, Fatma Hamieh, Alia Ng, Nathan |
| author_facet | Cicek, Fatma Hamieh, Alia Ng, Nathan |
| contents | In this article, we prove an asymptotic formula for the mean value of long smoothed Dirichlet polynomials with divisor coefficients. Our result has a main term that includes all lower order terms and a power saving error term. This is derived from a more general theorem on mean values of long smoothed Dirichlet polynomials that was previously established by the second and third authors. We thus establish a stronger form of a conjecture of Conrey and Gonek in the case of divisor functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_08057 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mean values of long Dirichlet polynomials with divisor coefficients Cicek, Fatma Hamieh, Alia Ng, Nathan Number Theory Primary 11M06, 11M26, 11M41, Secondary 11N37, 11N75 In this article, we prove an asymptotic formula for the mean value of long smoothed Dirichlet polynomials with divisor coefficients. Our result has a main term that includes all lower order terms and a power saving error term. This is derived from a more general theorem on mean values of long smoothed Dirichlet polynomials that was previously established by the second and third authors. We thus establish a stronger form of a conjecture of Conrey and Gonek in the case of divisor functions. |
| title | Mean values of long Dirichlet polynomials with divisor coefficients |
| topic | Number Theory Primary 11M06, 11M26, 11M41, Secondary 11N37, 11N75 |
| url | https://arxiv.org/abs/2309.08057 |