A universal estimate shows the singular product tail for Hardy-Littlewood and Bateman-Horn conjectures decays as 1/log regardless of system structure, with superfast convergence for linear cases and Galois-averaged coefficients for nonlinear ones under RH.
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Estimating the tail of the singular product for the Hardy Littlewood and Bateman Horn conjectures
A universal estimate shows the singular product tail for Hardy-Littlewood and Bateman-Horn conjectures decays as 1/log regardless of system structure, with superfast convergence for linear cases and Galois-averaged coefficients for nonlinear ones under RH.