Spectral Determinants, RG Fixed Points, and Determinantal Processes (Mathematics Version)

Key Points

• This research aims to create a framework for spectral operators in logarithmic prime lattices and explore links to the Riemann Hypothesis.
• Developed a rigorous framework for spectral operators defined on logarithmic prime lattices.
• Analyzed the correlation hierarchy under assumptions of positivity, translation invariance, and RG stability.
• Reformulated the Riemann Hypothesis using spectral conditions on a Fredholm determinant.
• Identified the sine kernel as the only determinantal limit of the correlation hierarchy under the stated assumptions.
• Established a spectral condition that reformulates the Riemann Hypothesis.

Abstract