E084: |ζ(1/2+it)| growth snapshots

E084 hero

E084: |ζ(1/2+it)| growth snapshots

Tags: analysis, quantitative-exploration, visualization, riemann-zeta, critical-line, numerics

Highlights

  • Focused numeric experiment with a single main figure.

  • Parameters saved to params.json for reproducibility.

  • Lightweight computation suitable for CI “slow” suite (small defaults).

What is computed

  • A parameterized numeric evaluation related to the Riemann zeta function.

  • A visualization summarizing the main phenomenon for the chosen parameter range.

Algorithm sketch

  1. Build the numeric grid / sampling points.

  2. Evaluate the target quantity with controlled truncation.

  3. Render the figure and write a short report.

Outputs

  • report.md — short narrative summary

  • params.json — experiment parameters snapshot

  • figures/fig_01_critical_line_logabs.png — main figure

Published run snapshot

If this experiment is included in the docs gallery, include the published snapshot (report + params).

We sample the magnitude of zeta(s) along the critical line s = 1/2 + i t on a moderate t-range.

params.json (snapshot)
{
  "mp_dps": 50,
  "n_points": 300,
  "t_max": 50.0
}

References

Edwards [1974], Titchmarsh [1986]