E109: Gauss sums: magnitude patterns

E109 hero

E109: Gauss sums: magnitude patterns

Tags: number-theory, dirichlet-characters, quantitative-exploration, visualization, 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

  • Compute Gauss sums τ(χ) and compare |τ(χ)| to √q.

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_gauss_sum_magnitudes.png

  • params.json

  • report.md

Notes

  • Nonprincipal characters: 9

  • max | |τ(χ)| - sqrt(q) |: 0.000000

  • For prime q, nonprincipal characters are primitive and |τ(χ)| = sqrt(q) (classic theorem).

params.json (snapshot)
{
  "q": 11
}

References

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