Note on the asymptotic of the auxiliary function
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929380274470912 |
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| author | de Reyna, Juan Arias |
| author_facet | de Reyna, Juan Arias |
| contents | To define an explicit regions without zeros of $\mathop{\mathcal R}(s)$, in a previous paper we obtained an approximation to $\mathop{\mathcal R}(s)$ of type $f(s)(1+U)$ with $|U|< 1$. But this $U$ do not tend to zero when $t\to+\infty$. In the present paper we get an approximation of the form $f(s)(1+o(t))$. We precise here Siegel's result, following his reasoning. This is essential to get the last Theorems in Siegel's paper about $\mathop{\mathcal R}(s)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Note on the asymptotic of the auxiliary function de Reyna, Juan Arias Number Theory Primary 11M06, Secondary 30D99 To define an explicit regions without zeros of $\mathop{\mathcal R}(s)$, in a previous paper we obtained an approximation to $\mathop{\mathcal R}(s)$ of type $f(s)(1+U)$ with $|U|< 1$. But this $U$ do not tend to zero when $t\to+\infty$. In the present paper we get an approximation of the form $f(s)(1+o(t))$. We precise here Siegel's result, following his reasoning. This is essential to get the last Theorems in Siegel's paper about $\mathop{\mathcal R}(s)$. |
| title | Note on the asymptotic of the auxiliary function |
| topic | Number Theory Primary 11M06, Secondary 30D99 |
| url | https://arxiv.org/abs/2406.06066 |