Published October 11, 2025 | Version version 4
Publication Open

A Graphical and Analytical Study of |χ(s)| and the Localization of Zeros of the Riemann ζ Function

  • 1. independant research

Description

Changes in version 4 (compared to v3, DOI: 10.5281/zenodo.18961451)

Mathematical changes:
- A new conjecture (Conjecture 3.1) has been added: "For any non-trivial zero s₀ of ζ(s), we have |χ(s₀)| = 1." This statement was not proved and remains a conjecture.
- The abstract has been rewritten to reflect this conditional nature.

Scripts and supplementary materials:
- Scripts for all figures are now included (10 Python + 4 SageMath files, standardised headers).
- README file finalized.
- All numerical experiments are reproducible.

Version identifier: v4

Files

chi_zeta_zero_localization.pdf

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Additional details

Dates

Accepted
2026-04-27
publication

Software

Development Status
Active