Framework for encoding modular forms and automorphic representations into spectral operators. For f (τ) = Σ aₙqⁿ of weight k and level N, constructs Hf whose spectral properties reflect the arithmetic of Fourier coefficients. Key innovations: Weight-Scaling Correspondence (modular weight → fractal dimension), Hecke-Spectral Isomorphism (Hecke eigenvalues → operator eigenvalues), Level Structure Encoding via boundary conditions. Applications to Ramanujan bounds, Sato-Tate distribution, modularity, and the Langlands program.
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Thierry Marechal
F5 Networks (United States)
F5 Networks (United States)
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Thierry Marechal (Wed,) studied this question.
synapsesocial.com/papers/69c6207d15a0a509bde18fbf — DOI: https://doi.org/10.5281/zenodo.19221610
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