Theorem of Spectral Localization for Arithmetic Mirror Wave Functions

Hello, In this article, I rigorously establish a spectral localization theorem for the discrete Fourier transform of arithmetic mirror wave functions of prime numbers (Corpus Mathematica). I show that the DFT exhibits a Lorentzian-shaped peak at a frequency determined by the imaginary part of γ and I clarify under which conditions this peak aligns with the modular inverse of 1 p. This result provides a solid mathematical foundation for the emerging field of arithmetic spectroscopy.CordialyCorpus Mathematica :https://doi.org/10.5281/zenodo.15967116