primitive Dirichlet character

本原狄利克雷特征

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Translation evidence: Literature usage

Meaning in context

A Dirichlet character modulo $N$ that is not induced from a character modulo any proper divisor of $N$.

模 $N$ 的狄利克雷特征，若不由模 $N$ 的任何真因子的特征诱导而来，则称其本原。

Example

The nontrivial character modulo $3$, with $\chi(1)=1$ and $\chi(2)=-1$, is primitive.

Usage and distinctions

Primitive means minimal modulus of induction; it does not mean a generator of the character group.

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Section 4.1.1, Definition 4.3, 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 导子和本原，printed page 103 · Checked 2026-10-14

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