On a mollifier of the perturbed Riemann zeta-function

Abstract

The mollification $\zeta (s)+{\zeta }^{\prime }(s)$ put forward by Feng is computed by analytic methods coming from the techniques of the ratios conjectures of $L$-functions. The current situation regarding the percentage of non-trivial zeros of the Riemann zeta-function on the critical line is then clarified.

33 pages, 1 Figure. Version 3: We have corrected some typos and have add a reference