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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2602.06080 |
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| _version_ | 1866908816668360704 |
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| author | Watson, Douglas F. |
| author_facet | Watson, Douglas F. |
| contents | We compare the Riemann $Ξ$--function to a canonical real-entire reference family arising from the cycle Laplacian developed in Paper I. These spectral determinants have only real zeros by self-adjointness. Our main tool is a rigidity lemma for holomorphic functions on horizontal strips. Applied to a normalized seam ratio linking $Ξ(2\cdot)$ to the reference family, this lemma shows that, under explicit holomorphy and boundary nonvanishing hypotheses verified in the forthcoming Paper III, the seam ratio extends to a zero-free holomorphic function of bounded type on each overlap strip. It follows that, on every admissible overlap strip, $Ξ(2\cdot)$ and the reference family have the same zero divisor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06080 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Riemann $Ξ$-function from primitive Markovian cycles II: Strip rigidity and divisor identification Watson, Douglas F. General Mathematics 11M26, 60J27, 26D15, 30D20 We compare the Riemann $Ξ$--function to a canonical real-entire reference family arising from the cycle Laplacian developed in Paper I. These spectral determinants have only real zeros by self-adjointness. Our main tool is a rigidity lemma for holomorphic functions on horizontal strips. Applied to a normalized seam ratio linking $Ξ(2\cdot)$ to the reference family, this lemma shows that, under explicit holomorphy and boundary nonvanishing hypotheses verified in the forthcoming Paper III, the seam ratio extends to a zero-free holomorphic function of bounded type on each overlap strip. It follows that, on every admissible overlap strip, $Ξ(2\cdot)$ and the reference family have the same zero divisor. |
| title | The Riemann $Ξ$-function from primitive Markovian cycles II: Strip rigidity and divisor identification |
| topic | General Mathematics 11M26, 60J27, 26D15, 30D20 |
| url | https://arxiv.org/abs/2602.06080 |