(SAPZ) Spectral and Arithmetic Perspectives on Generalized Zeta–like Functions: BMO and VMO Analysis of Hilbert Modular Newform L-Function Zero Gaps – v3.1

What’s new in v3.1

1. BMO/VMO analysis report (“BMO VMO analysis(full images).pdf”): added the full‐resolution figures and updated Table 1 to exactly match the numerical CSV.

2. High‐res versions of the GUE/BMO zero‐correlations paper (“Gue Bmo Zeta final3(Hi-resolution).pdf”) alongside the original lower‐res PDF.

3. Quantitative BMO spacing study (“Quant Bmo Zeros.pdf”): comprehensive treatment of quantitative BMO conditions, Jensen-type estimates, and numerical histograms.

4. Spectral zeta proposal v2 (“spectral_zeta_proposal_v2.pdf”): revised version of the general zero‐density framework with extended applications.

Contents of the bundle

• BMO & VMO analysis report (PDF, full & slim)

• GUE statistics and BMO zero‐correlations (PDF, hi-res & slim)

• Quantitative BMO zero‐spacing study (PDF)

• Spectral zeta proposal, revised v2 (PDF)

Summary of changes

• Table 1 in the VMO report now uses the exact numerical values from the uploaded CSV.

• All figures have been refreshed to high resolution and captions tightened.

• Added Abstract, Introduction, and cross-references in the VMO report for greater clarity.

• Minor typos and formatting fixes across all documents.

Recommended citation
Lee, B. (2025). Spectral and Arithmetic Perspectives on Generalized Zeta–like Functions: Selberg Class, Modular Forms, and Quantum Chaos. Zenodo, v3.1. https://doi.org/10.5281/zenodo.15510923