Number Theory

    

Prime Spectrum Model: Mapping Riemann Zeta Zeros to Prime Logarithms via Signal Processing

Authors: Trinh Tung Lam

The Prime Spectrum Model investigates the connection between the non-trivial zeros of the Riemann zeta function and the distribution of prime numbers using spectral analysis. A wave function is constructed from 40,000 zeros and analyzed using Fourier Transform and Short-Time Fourier Transform (STFT). Detected frequency peaks align with the natural logarithms of prime numbers, achieving RMSE = 0.0600 and Spearman correlation ≈ 1.0. The model successfully identifies the first 50 primes and extrapolates to higher ones. This work offers insights into the Riemann Hypothesis and opens applications in physics, signal processing, and complexity theory.

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[v1] 2025-05-19 01:46:49

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