I've read in a Bombieri's paper on official problem statement of Riemann hypothesis for Clay Math institute's millennium problems, a statement and what I understood of it is the following :

The Riemann hypothesis is equivalent to the statement that all local maxima of $ξ(t)$ are positive and all local minima are negative, and it has been suggested that if a counterexample exists then it should be in the neighborhood of unusually large peaks of $|ζ( 1/2 + it)|$.

Is there any current development around this approach ?

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