On a mollifier of the perturbed Riemann zeta-function

TL;DR

This paper analyzes a mollifier involving the Riemann zeta-function and its derivative, using advanced analytic techniques to clarify the distribution of its zeros on the critical line.

Contribution

It introduces and computes a new mollifier combining ta(s) and ta'(s) using ratios conjecture techniques, advancing understanding of zero distribution.

Findings

Clarifies the percentage of non-trivial zeros on the critical line.

Provides analytic computation of a novel mollifier.

Enhances methods for studying zeros of the Riemann zeta-function.

Abstract

The mollification $\zeta(s) + \zeta'(s)$ 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.