A proof of the Riemann hypothesis
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arXiv
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| Format: | Preprint |
| Published: |
2008
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| _version_ | 1866917005358006272 |
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| author | Li, Xian-Jin |
| author_facet | Li, Xian-Jin |
| contents | In this paper we study traces of an integral operator on two orthogonal subspaces of a $L^2$ space. One of the two traces is shown to be zero. Also, we prove that the trace of the operator on the second subspace is nonnegative. Hence, the operator has a nonnegative trace on the $L^2$ space. This implies the positivity of Li's criterion. By Li's criterion, all nontrivial zeros of the Riemann zeta-function lie on the critical line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0807_0090 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | A proof of the Riemann hypothesis Li, Xian-Jin General Mathematics 11M26, 11R56, 28A35, 30G06, 42B10, 47G10 In this paper we study traces of an integral operator on two orthogonal subspaces of a $L^2$ space. One of the two traces is shown to be zero. Also, we prove that the trace of the operator on the second subspace is nonnegative. Hence, the operator has a nonnegative trace on the $L^2$ space. This implies the positivity of Li's criterion. By Li's criterion, all nontrivial zeros of the Riemann zeta-function lie on the critical line. |
| title | A proof of the Riemann hypothesis |
| topic | General Mathematics 11M26, 11R56, 28A35, 30G06, 42B10, 47G10 |
| url | https://arxiv.org/abs/0807.0090 |