E122: Character averages over primes

E122 hero

E122: Character averages over primes

E122 hero

E122: Character averages over primes

E122 hero

E122: Character averages over primes

Tags: number-theory, dirichlet-characters, l-functions, quantitative-exploration, visualization, aps

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

  • Average χ(p) over primes in arithmetic progressions and compared to equidistribution heuristics.

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_mu_atlas.png

  • figures/fig_02_omega_atlas.png

  • figures/fig_03_phi_ratio_atlas.png

  • params.json

  • report.md

Notes

  • Atlas size: side=256 => N=65536

  • Visual textures encode multiplicativity and prime-power structure.

params.json (snapshot)
{
  "side": 256
}

References

  • See docs/background/dirichlet-characters.md.

  • See docs/background/dirichlet-l-functions.md and docs/background/dirichlet-convolution.md.

  • See docs/background/primes-in-arithmetic-progressions.md and docs/background/prime-number-races.md.