E106: Character gallery: real vs. complex

E106: Character gallery: real vs. complex

Tags: number-theory, dirichlet-characters, visualization, multiplicative

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

• Compare value-sets of Dirichlet characters and count real-valued characters.

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_real_character_counts.png

• params.json

• report.md

Notes

• q values: [5, 8, 10, 12, 15]

• real/total: [(5, 2, 4), (8, 4, 4), (10, 2, 4), (12, 4, 4), (15, 4, 8)]

• Real characters correspond to quadratic characters and products thereof.

params.json (snapshot)

{
  "q_values": [
    5,
    8,
    10,
    12,
    15
  ]
}

References

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

Related experiments

• E108: Orthogonality heatmap for characters (E108: Orthogonality heatmap for characters)

• E064: Dirichlet character tables (phase view). (Dirichlet character tables (phase view).)

• E066: Character partial sums: cancellation profiles. (Character partial sums: cancellation profiles.)

• E077: Indicator via character orthogonality (sanity check). (Indicator via character orthogonality (sanity check).)

• E122: Character averages over primes (E122: Character averages over primes)