Golden Ratio's Hidden Arithmetic Resonance with Möbius and Totient — E8 Intelligence Research

Q: What does this research mean for the field?

A 'golden pair of identities' mathematically links the golden ratio to the Möbius function, Euler's totient, and the natural logarithm via Dirichlet convolution. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22701591

September 11, 2026Open Access

Golden Ratio's Hidden Arithmetic Resonance with Möbius and Totient — E8 Intelligence Research

View Full Paper

Ask AI

Bookmark

Share

Key Points

Investigate analytic identities that link the golden ratio φ to fundamental arithmetic functions, including the Möbius function and Euler's totient.
Formulated infinite series representations combining exponential powers of the golden ratio with multiplicative arithmetic functions.
Applied Dirichlet convolution, the Möbius inversion formula, and connections to modular forms such as the Dedekind eta function.
Demonstrated an identity linking the Möbius function and powers of φ to the natural logarithm via the convergent series ∑_{n=1}^∞ μ(n) · (φ^n − 1)⁻¹ = ln(φ).
Established related harmonic series for Euler's totient φ(n) connecting logarithmic expressions to modular forms and the Dedekind eta function.

No abstract yet

We only have this paper's title and publication details.

Read it at the source

Ask about this paper

Answers are grounded in this paper and cite their sources.

Implication

Theoretical analysis reveals identities connecting the golden ratio to arithmetic functions via Dirichlet convolution, suggesting hidden structural harmony in number theory.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6aa7b3440926e14a848b21b6 https://doi.org/10.5281/zenodo.22701591

View Full Paper

Ask AI

Bookmark

Share

Golden Ratio's Hidden Arithmetic Resonance with Möbius and Totient — E8 Intelligence Research

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

Golden Ratio's Hidden Arithmetic Resonance with Möbius and Totient — E8 Intelligence Research

Key Points

No abstract yet

Ask about this paper

Implication

Discussion

Cite This Study

Keep reading

Keep reading