E089: log|ζ(s)| heatmap

E089 hero

E089: log|ζ(s)| heatmap

Tags: analysis, quantitative-exploration, visualization, riemann-zeta, 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_zeta_heatmap_logabs.png — main figure

Published run snapshot

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

We plot log10|zeta(s)| on a coarse grid in the (sigma, t) plane. The pole at s=1 manifests as a bright region near sigma=1, t=0.

params.json (snapshot)
{
  "mp_dps": 50,
  "n_sigma": 31,
  "n_t": 41,
  "sigma_max": 2.0,
  "sigma_min": 0.0,
  "t_max": 20.0,
  "t_min": -20.0
}

References

Edwards [1974], Titchmarsh [1986]