An extension to the complex plane of the Riemann-Siegel Z function
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866910705681170432 |
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| author | Lodone, Giovanni |
| author_facet | Lodone, Giovanni |
| contents | The usual Riemann-Siegel Z(t) is a real-valued function. We construct a complex function depending from t and from distance from critical line. It is linked to Riemann Xi(s) function by the same real scaling factor of the usual Riemann-Siegel Z(t) on critical line. Errors are not greater than the errors of Riemann-Siegel Z(t) on the critical line, while this result covers at least the whole critical strip. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_03191 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | An extension to the complex plane of the Riemann-Siegel Z function Lodone, Giovanni Classical Analysis and ODEs 11M06, 11M26, 11M99 The usual Riemann-Siegel Z(t) is a real-valued function. We construct a complex function depending from t and from distance from critical line. It is linked to Riemann Xi(s) function by the same real scaling factor of the usual Riemann-Siegel Z(t) on critical line. Errors are not greater than the errors of Riemann-Siegel Z(t) on the critical line, while this result covers at least the whole critical strip. |
| title | An extension to the complex plane of the Riemann-Siegel Z function |
| topic | Classical Analysis and ODEs 11M06, 11M26, 11M99 |
| url | https://arxiv.org/abs/2107.03191 |