A proof of Riemann Hypothesis
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866917685448671232 |
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| author | Niu, Pengcheng Zhang, Junli |
| author_facet | Niu, Pengcheng Zhang, Junli |
| contents | Let $Ξ(t)$ be a function relating to the Riemann zeta function $ζ(s)$ with $s = \frac{1} {2} + it$. In this paper, we construct a function $v$ containing $t$ and $Ξ(t)$, and prove that $v$ satisfies a nonadjoint boundary value problem to a nonsingular differential equation if $t$ is any nontrivial zero of $Ξ(t)$. Inspecting properties of $v$ and using known results of nontrivial zeros of $ζ(s)$, we derive that nontrivial zeros of $ζ(s)$ all have real part equal to $\frac{1} {2}$, which concludes that Riemann Hypothesis is true. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1704_05747 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A proof of Riemann Hypothesis Niu, Pengcheng Zhang, Junli General Mathematics 11M26 Let $Ξ(t)$ be a function relating to the Riemann zeta function $ζ(s)$ with $s = \frac{1} {2} + it$. In this paper, we construct a function $v$ containing $t$ and $Ξ(t)$, and prove that $v$ satisfies a nonadjoint boundary value problem to a nonsingular differential equation if $t$ is any nontrivial zero of $Ξ(t)$. Inspecting properties of $v$ and using known results of nontrivial zeros of $ζ(s)$, we derive that nontrivial zeros of $ζ(s)$ all have real part equal to $\frac{1} {2}$, which concludes that Riemann Hypothesis is true. |
| title | A proof of Riemann Hypothesis |
| topic | General Mathematics 11M26 |
| url | https://arxiv.org/abs/1704.05747 |