Riemann Hypothesis

Prove that all non-trivial zeros of the Riemann zeta function ζ(s) lie on the critical line Re(s) = 1/2.

Background

The paper recalls the classical Riemann Hypothesis (RH) as the central problem motivating the development of a new variational framework for relating zeros of the core function Z0(t)=cos(θ(t)) to zeros of the Hardy Z-function Z(t).

Throughout the work, the author explores Edwards’ speculation and proposes a high-dimensional variational approach via sections ZN(t; ā), recasting RH as an optimization problem about maintaining reality of zeros along paths in parameter space.