What question did this study set out to answer?

The aim is to develop a framework to analyze the distribution of non-trivial zeros of the Riemann zeta function.

May 26, 2026Open Access

A Curvature Decomposition of the Explicit Formula for the Riemann Zeta Function

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The aim is to develop a framework to analyze the distribution of non-trivial zeros of the Riemann zeta function.
Analyzed the second logarithmic derivative of the completed zeta function.
Established a prime-cutoff decomposition into archimedean and local curvature contributions.
Verified numerical ratios related to local curvature and critical divergence patterns.
Local positivity V_p(σ) ≥ 0 established for all primes p and σ > 0.
Critical divergence H_local(½,κ) ~ 2(log κ)² demonstrated for truncated local curvature.
Convergence H_local(σ,κ) confirmed for all σ > ½, establishing σ = ½ as a unique phase boundary.

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Implication

This theoretical framework explores local curvature contributions of the Riemann zeta function, highlighting critical divergence and convergence patterns.

Cite This Study

Ulrich Tehrani (2026) studied this question.

synapsesocial.com/papers/6a153a2eb5d9c58d83e8cfeb https://doi.org/10.5281/zenodo.20362830

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Implication

This theoretical framework explores local curvature contributions of the Riemann zeta function, highlighting critical divergence and convergence patterns.

A Curvature Decomposition of the Explicit Formula for the Riemann Zeta Function

Key Points

Discussion

Implication

Cite This Study

A Curvature Decomposition of the Explicit Formula for the Riemann Zeta Function

Key Points

Discussion

Implication

Cite This Study

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