What question did this study set out to answer?

To explore the relationships between geometric gnomons and the distribution of prime numbers in short intervals using the Non-Linear Maier Matrix Method.

August 4, 2026Open Access

The Non-Linear Maier Matrix Method: Geometric Gnomons, Hessian Amplification, and the Spectral-Geometric Resonance of the Riemann Zeros

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HVHuynh Hai Dang Vo

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Implication

Randomized trial identifies geometric gnomon structures affecting the prime distribution based on Riemann zeros, suggesting new avenues for exploration.

Key Points

To explore the relationships between geometric gnomons and the distribution of prime numbers in short intervals using the Non-Linear Maier Matrix Method.
Introduced two-parameter polygonal gnomon numbers $A_{m,j}, W_{m,j}$ for intervals $I_{m,j}$.
Analyzed asymptotic behavior of these arrays against the Iwaniec--Laborde theorem on almost-primes.
Conducted numerical experiments with non-trivial zeros of the zeta function to observe the behavior of the integral bound.
$I_{m,j}$ demonstrates a geometric surplus of order $j^{0.55}m^{0.1}$, effectively guaranteeing the presence of a $P_2$-number for large $m$.
Identified a constant inflation of order $m^{2/3}$ in the effective bound which exceeds geometric surplus, complicating the analysis.
Established a continuous double integral bound $|I(N)| ext{ in dyadic blocks satisfies } |I(N)| ext{ is bounded by }6J(2M+3J)/N^2.

Cite This Study

Huynh Hai Dang Vo (2026) studied this question.

synapsesocial.com/papers/6a71b6afc47350ef8e494dbb https://doi.org/10.5281/zenodo.21758720

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Implication

Randomized trial identifies geometric gnomon structures affecting the prime distribution based on Riemann zeros, suggesting new avenues for exploration.

The Non-Linear Maier Matrix Method: Geometric Gnomons, Hessian Amplification, and the Spectral-Geometric Resonance of the Riemann Zeros

Discussion

Member takes

Implication

Key Points

Cite This Study

The Non-Linear Maier Matrix Method: Geometric Gnomons, Hessian Amplification, and the Spectral-Geometric Resonance of the Riemann Zeros

Discussion

Member takes

Implication

Key Points

Cite This Study

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