Sandwiching the Riemann hypothesis

R. C. McPhedran

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arXiv · 2407.00060

Sandwiching the Riemann hypothesis

R. C. McPhedran

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Abstract

We consider a system of three analytic functions, two of which are known to have all their zeros on the critical line $\Re (s)=\sigma=1/2$. We construct inequalities which constrain the third function, $\xi(s)$, 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 $\xi(s)$, with promising results.

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R. C. McPhedran. 2024-06-16. Sandwiching the Riemann hypothesis. https://arxiv.org/abs/2407.00060

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