conductor of a Dirichlet character

狄利克雷特征的导子

Number Theory · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: Dirichlet-character conductor

Translation evidence: Literature usage

Meaning in context

For a character modulo $N$, the least positive divisor $f$ of $N$ from whose character group it is induced by reduction of units.

对模 $N$ 的特征，其导子是使该特征可由模 $f$ 的特征经单位群约化映射诱导而来的最小正因子 $f\mid N$。

Example

The character modulo $8$ with values $1,-1,1,-1$ at $1,3,5,7$ has conductor $4$.

Usage and distinctions

The displayed modulus may exceed the conductor; extensions by zero at nonunits need not agree as integer-valued functions at primes removed from the modulus.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义Definition 4.3 and Example 4.1(1), printed page 103 · Checked 2026-10-14

Translation sources

1. 张神星 — 代数数论讲义 v2.5 (2024-01-09)，合肥工业大学作者讲义定义4.3 导子，例题4.1(1)，printed page 103 · Checked 2026-10-14

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