Algebraic Number Theory
《Algebraic Number Theory》 · 第 109 页 · Section 4.1「Additive characters」
These functions are called the additive characters (mod $q$) because they are the homomorphisms from the additive group $(\mathbb Z/q\mathbb Z)^+$ of integers (mod $q$) to the multiplicative group $\mathbb C^\times$ of non-zero complex numbers.