The Riemann $Ξ$-function from primitive Markovian cycles II: Strip rigidity and divisor identification

Douglas F. Watson

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arXiv · 2602.06080

The Riemann $Ξ$-function from primitive Markovian cycles II: Strip rigidity and divisor identification

Douglas F. Watson

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Abstract

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.

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Douglas F. Watson. 2026-02-04. The Riemann $Ξ$-function from primitive Markovian cycles II: Strip rigidity and divisor identification. https://arxiv.org/abs/2602.06080

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