E114: ζ via η: stability map on the critical line

E114 hero

E114: ζ via η: stability map on the critical line

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

Highlights

  • Focused numeric experiment with a small set of figures.

  • Parameters saved to params.json for reproducibility.

  • Defaults are chosen, so the experiment remains feasible for the CI “slow” suite.

What is computed

  • Study stability of ζ(1/2+it) via η-acceleration under truncation changes.

Notes

  • This page summarizes the intent; see the generated report.md in out/ for concrete outputs.

Published run snapshot

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

Artifacts

  • figures/fig_01_eta_truncation_errors.png

  • params.json

  • report.md

Notes

  • n_terms -> max error: {100: ‘1.20e-01’, 200: ‘8.52e-02’, 400: ‘6.03e-02’}

  • η-series converges for Re(s)>0, but near Re(s)=1/2 the truncation error is still visible.

params.json (snapshot)
{
  "eval_dps": 50,
  "n_terms_values": [
    100,
    200,
    400
  ],
  "ref_dps": 70,
  "t_max": 30.0,
  "t_steps": 61
}

References

  • See the zeta / zeros background pages in docs/background/.