Sandwiching the Riemann hypothesis
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909308345647104 |
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| author | McPhedran, R. C. |
| author_facet | McPhedran, R. C. |
| contents | We consider a system of three analytic functions, two of which are known to have all their zeros on the critical line $\Re (s)=σ=1/2$. We construct inequalities which constrain the third function, $ξ(s)$, on $\Im(s)=0$ to lie between the other two functions, in a sandwich structure. We investigate what can be said about the location of zeros and radius of convergence of expansions of $ξ(s)$, with promising results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sandwiching the Riemann hypothesis McPhedran, R. C. General Mathematics 11M26 We consider a system of three analytic functions, two of which are known to have all their zeros on the critical line $\Re (s)=σ=1/2$. We construct inequalities which constrain the third function, $ξ(s)$, on $\Im(s)=0$ to lie between the other two functions, in a sandwich structure. We investigate what can be said about the location of zeros and radius of convergence of expansions of $ξ(s)$, with promising results. |
| title | Sandwiching the Riemann hypothesis |
| topic | General Mathematics 11M26 |
| url | https://arxiv.org/abs/2407.00060 |