The first Hankel relaxation Riemann hypothesis

With Λ\Lambda as above, for real xx define

Λ(x)2Λ(x)Λ(x).\Lambda'(x)^2-\Lambda”(x)\Lambda(x).

First Hankel relaxation Riemann hypothesis.

Λ(x)2Λ(x)Λ(x)0\Lambda'(x)^2-\Lambda”(x)\Lambda(x)\geq 0

for real xx. This is the N=1N=1 case of the Hankel relaxation hierarchy and was originally conjectured by Csordas; the source gives no resolution.

Sources & referencesView supporting material

Primary source

Kelly Bickel, J. E. Pascoe and Meredith Sargent, “Zero-free regions near a line”, arXiv:2108.04807 (2021).

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