A Spectral Construction Toward the Riemann Hypothesis

Key Points

• To propose a spectral construction aligned with the Riemann Hypothesis using a self-adjoint operator.
• Defined a self-adjoint operator replicating the imaginary parts of Riemann zeta function zeros.
• Combined inverse spectral theory with the classical explicit formula.
• Established a trace relation related to prime number distribution.
• Implemented a positivity condition following Weil’s criterion.
• Developed an operator-theoretic structure consistent with the Riemann Hypothesis.
• Showed that the spectrum of the operator aligns with non-trivial zeros of the zeta function.
• Demonstrated a coherent relationship between trace relations and prime distribution.