E104: von Mangoldt Λ(n): support and statistics

E104 hero

E104: von Mangoldt Λ(n): support and statistics

Tags: number-theory, quantitative-exploration, visualization, mangoldt, arithmetic-functions

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

  • Visualize where Λ(n) is nonzero (prime powers) and summarize basic statistics.

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_lambda_hist.png

  • params.json

  • report.md

Notes

  • Nonzero density: 0.090600

  • Unique Λ(n) values are logs of primes; sample: [0.69314718, 1.09861229, 1.60943791, 1.94591015, 2.39789527, 2.56494936, 2.83321334, 2.94443898, 3.13549422, 3.36729583]

params.json (snapshot)
{
  "bins": 30,
  "n_max": 200000
}

References

  • See the arithmetic-functions background pages in docs/background/.