E120: Liouville λ(n): partial sums and parity

E120 hero

E120: Liouville λ(n): partial sums and parity

Tags: number-theory, quantitative-exploration, visualization, liouville, omega

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

  • Explore partial sums of the Liouville function and simple parity correlations.

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_pretentious_distance_proxy.png

  • params.json

  • report.md

Notes

  • Final value (principal): 0.000000

  • Final value (nonprincipal): 2.881212

  • This is a toy version of the pretentious distance framework (Granville–Soundararajan).

params.json (snapshot)
{
  "p_max": 400000,
  "q": 8
}

References

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