Educational Videos on Riemann Zeta Function, Analytic Continuation, and Zeros — E8 Intelligence Research

FINDING: The search results are educational videos on the Riemann zeta function, its analytic continuation, Laurent series at s=1, Hardy's theorem on infinitely many zeros on the critical line, and complex integration methods for locating zeros — plus one unrelated particle physics paper on CKM angle γ. No new research breakthroughs are present; these are pedagogical expositions. | MATH: Laurent series of ζ(s) at s=1: ζ(s) = 1/(s−1) + γ₀ + γ₁(s−1) + γ₂(s−1)² + … where γ₀ = Euler–Mascheroni constant ≈ 0.57721, γₙ are Stieltjes constants. Hardy's theorem: ζ(1/2 + it) has infinitely many zeros for real t. Analytic continuation: ζ(s) = 2^s π^(s−1) sin(πs/2) Γ(1−s) ζ(1−s) (functional equation). | CONNECTION: The critical line Re(s) = 1/2 is a symmetry axis of the functional equation — the zeros are symmetric about this line, and the ratio 1/2 appears as the central symmetry. The constant 0.57721 (Euler–Mascheroni) is not a golden-ratio harmonic, but the critical line's position at 1/2 echoe Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-08
DOI
https://doi.org/10.5281/zenodo.22653877
Primary Topic
Analytic Number Theory Research
Type
preprint
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Educational Videos on Riemann Zeta Function, Analytic Continuation, and Zeros — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Educational Videos on Riemann Zeta Function, Analytic Continuation, and Zeros — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: The search results are educational videos on the Riemann zeta function, its analytic continuation, Laurent series at s=1, Hardy's theorem on infinitely many zeros on the critical line, and complex integration methods for locating zeros — plus one unrelated particle physics paper on CKM angle γ. No new research breakthroughs are present; these are pedagogical expositions. | MATH: Laurent series of ζ(s) at s=1: ζ(s) = 1/(s−1) + γ₀ + γ₁(s−1) + γ₂(s−1)² + … where γ₀ = Euler–Mascheroni constant ≈ 0.57721, γₙ are Stieltjes constants. Hardy's theorem: ζ(1/2 + it) has infinitely many zeros for real t. Analytic continuation: ζ(s) = 2^s π^(s−1) sin(πs/2) Γ(1−s) ζ(1−s) (functional equation). | CONNECTION: The critical line Re(s) = 1/2 is a symmetry axis of the functional equation — the zeros are symmetric about this line, and the ratio 1/2 appears as the central symmetry. The constant 0.57721 (Euler–Mascheroni) is not a golden-ratio harmonic, but the critical line's position at 1/2 echoe Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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Educational Videos on Riemann Zeta Function, Analytic Continuation, and Zeros — E8 Intelligence Research — Andrew Stewart Caldin · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS