Symmetry-Based Proof of the Generalized Riemann Hypothesis

This paper presents a symmetry-based approach to the Generalized Riemann Hypothesis, focusing on the structure of nontrivial zeros of the completed Dirichlet L-function. By examining the relationship between the functional equation and complex conjugation, the argument shows that each nontrivial zero implies the existence of a symmetrically paired zero. This pairing, when interpreted through a restricted application of the Schwarz Reflection Principle at the zero points, leads to the conclusion that all nontrivial zeros must lie on the critical line. The analysis is further extended to generalized cases, including product forms, which consistently reduce to the same critical line condition. This work therefore proposes a comprehensive and logically consistent framework that supports the truth of the Generalized Riemann Hypothesis.