What question did this study set out to answer?

This work aims to explain the GUE statistics observed in the zeros of the Riemann zeta function through structural means rather than dynamical models.

August 1, 2026Open Access

Arithmetic Holonomy and Non-Integrable Accumulation as a Structural Origin of GUE Statistics in the Zeros of the Riemann Zeta Function

View Full Paper

Ask AI

Bookmark

Authors

LDLaurent Danion

Discussion

Member takes

Implication

Exploratory work proposes structural origins of GUE statistics in the Riemann zeta function zeros, implying a new viewpoint.

Key Points

This work aims to explain the GUE statistics observed in the zeros of the Riemann zeta function through structural means rather than dynamical models.
Introduced concept of arithmetic holonomy as a structural viewpoint.
Explored non-integrability of arithmetic accumulation in relation to GUE statistics.
Examined admissible accumulation procedures and their impact on level repulsion and spectral rigidity.
Proposed that non-vanishing holonomy leads to local desynchronization (level repulsion) and global rigidity.
Demonstrated that prevailing Hamiltonian dynamics are unnecessary for explaining spectral properties.

Cite This Study

Laurent Danion (2026) studied this question.

synapsesocial.com/papers/6a6d97c4e258b358b3c6a9c2 https://doi.org/10.5281/zenodo.18186625

View Full Paper

Ask AI

Bookmark

Arithmetic Holonomy and Non-Integrable Accumulation as a Structural Origin of GUE Statistics in the Zeros of the Riemann Zeta Function

Discussion

Member takes

Implication

Key Points

Cite This Study

Arithmetic Holonomy and Non-Integrable Accumulation as a Structural Origin of GUE Statistics in the Zeros of the Riemann Zeta Function

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider