420 research outputs found
A New Discriminant for the Hardy Z-Function and the Corrected Gram's law
In this paper, we introduce a novel variational framework rooted in algebraic
geometry for the analysis of the Hardy -function. Our primary contribution
lies in the definition and exploration of , a newly
devised discriminant that measures the realness of consecutive zeros of .
Our investigation into and its properties yields a
wealth of compelling insights into the zeros of , including the corrected
Gram's law, the second-order approximation of , and the
discovery of the G-B-G repulsion relation. Collectively, these results provide
compelling evidence supporting a new plausibility argument for the Riemann
hypothesis
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