Spectral Phase Tracking and Harmonic Interference Modeling of Prime Distributions Along the Critical Line

The distribution of prime numbers is traditionally analyzed through the lens of analytic number theory, heavily relying on the Prime Number Theorem and the logarithmic integral. In this exploratory paper, we approach prime distribution and the Riemann Zeta function purely from a signal processing and harmonic resonance perspective. By modeling the prime counting error term as a deterministic spectral deviation, and visualizing the Zeta function on the critical line as a coupled harmonic oscillator, we highlight the intrinsic periodicities of the prime sequence. We provide numerical visualizations demonstrating that structural irregularities in prime distributions can be geometrically mapped as predictable interference patterns, offering a didactic bridge between abstract analytic number theory and applied harmonic analysis.