Langlands Functoriality and the Riemann Hypothesis: A Unified Spectral Framework
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| Formato: | Recurso digital |
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2025
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| _version_ | 1866902087533592576 |
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| author | Mercer, Jason David John |
| author_facet | Mercer, Jason David John |
| contents | <p>This paper explores the implications of Langlands Functoriality for the Riemann Hypothesis (RH) and the Generalized Riemann Hypothesis (GRH). By developing a spectral framework using automorphic constraints, modular symmetries, and numerical validation, we analyze classical L-functions, higher-dimensional zeta functions, and their spectral scaling behaviors. Our results provide strong evidence that Langlands principles enforce zero alignment on critical lines and hyperplanes, supporting RH and GRH.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_14760775 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Langlands Functoriality and the Riemann Hypothesis: A Unified Spectral Framework Mercer, Jason David John Langlands Functoriality Riemann Hypothesis (RH) Generalized Riemann Hypothesis (GRH) High-Rank L-Function Validation Prime Distribution & Lattice Harmonics Cyclic Balance & Spectral Harmony Quantum Physics & Spectral Chaos Number Theory in Quantum Systems The Music of the Primes A Universal Dance of Harmonics The Hidden Order Beneath Infinity <p>This paper explores the implications of Langlands Functoriality for the Riemann Hypothesis (RH) and the Generalized Riemann Hypothesis (GRH). By developing a spectral framework using automorphic constraints, modular symmetries, and numerical validation, we analyze classical L-functions, higher-dimensional zeta functions, and their spectral scaling behaviors. Our results provide strong evidence that Langlands principles enforce zero alignment on critical lines and hyperplanes, supporting RH and GRH.</p> |
| title | Langlands Functoriality and the Riemann Hypothesis: A Unified Spectral Framework |
| topic | Langlands Functoriality Riemann Hypothesis (RH) Generalized Riemann Hypothesis (GRH) High-Rank L-Function Validation Prime Distribution & Lattice Harmonics Cyclic Balance & Spectral Harmony Quantum Physics & Spectral Chaos Number Theory in Quantum Systems The Music of the Primes A Universal Dance of Harmonics The Hidden Order Beneath Infinity |
| url | https://doi.org/10.5281/zenodo.14760775 |