The Extended Zeta Function: Helical Lorentz Structure, Gaussian Emergence, Phase-Shifted Spherical Envelopes, Analytic Wave Coupling, and Internal Γ-Landau-vs. External ε-Hurwitz-Drift

The Extended Zeta Function: Helical Lorentz Structure, Gaussian Emergence, Phase-Shifted Spherical Envelopes, Analytic Wave Coupling, and Internal Γ-Landau-vs. External ε-Hurwitz-Drift | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 15 October 2025 V1 Latest version Share on The Extended Zeta Function: Helical Lorentz Structure, Gaussian Emergence, Phase-Shifted Spherical Envelopes, Analytic Wave Coupling, and Internal Γ-Landau-vs. External ε-Hurwitz-Drift Author : Thomas Richter 0009-0007-4180-9817 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176055040.09519231/v1 199 views 148 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We develop a purely analytic framework linking polylogarithmic representations to formal structures reminiscent of relativity, quantum mechanics, and thermodynamics. Via analytic continuation of phase parameters we introduce a helical-hyperbolic analogy: a strictly mathematical invariance whose stationary-phase geometry produces Gaussian envelopes at the fractional-Fourier angles ϕ ∈ π 4 + π 2 Z. The associated phase-shifted spherical envelopes appear as conjugate helices whose superposition produces a standing Gaussian profile. A Mellin-Hurwitz projection isolates two infinitesimal deformation modes-an internal Γ-Landau and an external ε-Hurwitz drift. The analogies discussed below are formal correspondences within analytic function theory; any possible physical implications would require independent empirical validation. Supplementary Material File (zeta_gauss.pdf) Download 400.46 KB Information & Authors Information Version history V1 Version 1 15 October 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords cosmology general relativity mathematical physics quantum mechanics riemann zeta thermodynamics unified physics unified theory zeta function Authors Affiliations Thomas Richter 0009-0007-4180-9817 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 199 views 148 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Thomas Richter. The Extended Zeta Function: Helical Lorentz Structure, Gaussian Emergence, Phase-Shifted Spherical Envelopes, Analytic Wave Coupling, and Internal Γ-Landau-vs. External ε-Hurwitz-Drift. Authorea . 15 October 2025. 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