On the Phragmen Lindelöf Theorem in strips
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910186066673664 |
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| author | Smith, Kevin |
| author_facet | Smith, Kevin |
| contents | In this paper we study an $L^{p}$ analogue of Bohr's abscissae of summability for Dirichlet series. For polynomially bounded analytic functions in a strip with order function $μ$, convexity of $1/μ$ is equivalent to approximate concavity of the abscissae in $p$. If $μ$ obeys a functional equation of the Selberg class type, this is equivalent to the Lindelöf hypothesis if $μ'(1/2)$ does not exist. Otherwise, $μ$ is everywhere differentiable (therefore subconvex) with quadratic decay near one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17064 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Phragmen Lindelöf Theorem in strips Smith, Kevin Complex Variables 11M99 (Primary) 30A99 (Secondary) In this paper we study an $L^{p}$ analogue of Bohr's abscissae of summability for Dirichlet series. For polynomially bounded analytic functions in a strip with order function $μ$, convexity of $1/μ$ is equivalent to approximate concavity of the abscissae in $p$. If $μ$ obeys a functional equation of the Selberg class type, this is equivalent to the Lindelöf hypothesis if $μ'(1/2)$ does not exist. Otherwise, $μ$ is everywhere differentiable (therefore subconvex) with quadratic decay near one. |
| title | On the Phragmen Lindelöf Theorem in strips |
| topic | Complex Variables 11M99 (Primary) 30A99 (Secondary) |
| url | https://arxiv.org/abs/2502.17064 |