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Proposes a framework for examining modular reflection and zeta zeros in Mellin geometry, suggesting new implications for number theory.
This paper proposes a second-quantized and operator-theoretic framework for studying modular reflection and zeta zeros in Mellin geometry. The Dirichlet eta function is interpreted as a fermionically graded arithmetic source, and modular invariance together with zero-support conditions are formulated as formal BRST constraints in a rigged-Hilbert-space setting. The associated BRST heat-semigroup projection is used as a formal mechanism for extracting a BRST-harmonic arithmetic sector. The paper does not claim to prove the Riemann Hypothesis. Instead, it reformulates part of the critical-line problem as a spectral realization problem: whether zero-supported distributional Mellin modes associated with zeta zeros can be related to normalizable or suitably regularized BRST-harmonic spectral representatives compatible with modular reflection. An Explanatory Note for Number Theorists about BRST Cohomology and Heat Flow: https://note.com/kafukanoochan/n/na294e0ca4ee9
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hideo umihara (2026) studied this question.
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