E115: Hardy Z: sign changes and zero bracketing

E115 hero

E115: Hardy Z: sign changes and zero bracketing

Tags: analysis, quantitative-exploration, visualization, riemann-zeta, hardy-z, zeta-zeros

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

  • Scan Hardy Z(t), bracket sign changes, and visualize candidate zeros.

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_hardy_Z_scan.png

  • params.json

  • report.md

Notes

  • Sign-change intervals (first 12): [(14.100000000000001, 14.200000000000001), (21.0, 21.1), (25.0, 25.1), (30.400000000000002, 30.5), (32.9, 33.0), (37.5, 37.6)]

  • Each sign change suggests a zero of ζ(1/2+it) in that interval.

params.json (snapshot)
{
  "dps": 40,
  "dt": 0.1,
  "t_max": 40.0
}

References

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