DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-05

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

The principal character modulo q

Definition

For $q \geq 1$ , the principal Dirichlet character modulo $q$ is the character $χ_{0}$ modulo $q$ defined by

$χ_{0} (n) = {\begin{cases} 1, & (n, q) = 1, \\ 0, & (n, q) > 1. \end{cases}$

Equivalently, its underlying homomorphism on $(Z / q Z)^{\times}$ is the trivial group homomorphism.

Depends on

Dirichlet characters modulo q

Used by

Dependency tree · one level

1 result within one dependency step of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Kiran S. Kedlaya, Notes on Analytic Number Theory, section 3.1 (standard reference, not scraped)
Andrew V. Sutherland, Number Theory I, Definition 18.11 (standard reference, not scraped)