Under RH and a pole-damping width bound, a Gaussian–Perron prime-side defect near each fixed simple critical-line zero equals −a Re(e^{−λ}/λ) up to an exponentially small nonlocal error.
Note on the positivity of the real part of the log-derivative of the Riemannξ-function near the critical line
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A Gaussian-Perron Prime-Side Defect and Local Profiles Near Critical-Line Zeros of the Riemann Zeta Function
Under RH and a pole-damping width bound, a Gaussian–Perron prime-side defect near each fixed simple critical-line zero equals −a Re(e^{−λ}/λ) up to an exponentially small nonlocal error.