A Potential-Theoretic Approach to the Location of Zeros of the Riemann Zeta Function

This paper presents a potential-theoretic approach to analyze the nontrivial zeros of the Riemann zeta function. We introduce an auxiliary function that incorporates the zeta function within a carefully chosen non-holomorphic factor. By applying classical methods from potential theory, we demonstrate strict subharmonicity properties of the modulus of this auxiliary function in specific regions of the complex plane. Utilizing the strong minimum principle for subharmonic functions, we systematically exclude the possibility of zeros of the zeta function lying off the critical line. This approach provides a novel perspective on the Riemann hypothesis by framing the classical conjecture within the language of subharmonic functions and distribution theory.