An investigation of the non-trivial zeros of the Riemann zeta function
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arXiv
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866929346185265152 |
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| author | Heymann, Yuri |
| author_facet | Heymann, Yuri |
| contents | While many zeros of the Riemann zeta function are located on the critical line $\Re(s)=1/2$, the non-existence of zeros in the remaining part of the critical strip $\Re(s) \in \, ]0, 1[$ is the main scope to be proven for the Riemann hypothesis. The Riemann zeta functional leads to a relation between the zeros on either sides of the critical line. Given $s$ a complex number and $\bar{s}$ its complex conjugate, if $s$ is a zero of the Riemann zeta function in the critical strip $\Re(s) \in \, ]0, 1[$, then $ζ(s) = ζ(1-\bar{s})$, as a key proposition to prove the Riemann hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1804_04700 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An investigation of the non-trivial zeros of the Riemann zeta function Heymann, Yuri General Mathematics 11M06 While many zeros of the Riemann zeta function are located on the critical line $\Re(s)=1/2$, the non-existence of zeros in the remaining part of the critical strip $\Re(s) \in \, ]0, 1[$ is the main scope to be proven for the Riemann hypothesis. The Riemann zeta functional leads to a relation between the zeros on either sides of the critical line. Given $s$ a complex number and $\bar{s}$ its complex conjugate, if $s$ is a zero of the Riemann zeta function in the critical strip $\Re(s) \in \, ]0, 1[$, then $ζ(s) = ζ(1-\bar{s})$, as a key proposition to prove the Riemann hypothesis. |
| title | An investigation of the non-trivial zeros of the Riemann zeta function |
| topic | General Mathematics 11M06 |
| url | https://arxiv.org/abs/1804.04700 |