quality:correction, structural:expansion
Chudakov's Condition

A Dirichlet character is a completely multiplicative function f: N → C {\displaystyle f:\mathbb {N} \rightarrow \mathbb {C} } satisfying the following three properties: a) f {\displaystyle f} takes only finitely many values; b) f {\displaystyle f} vanishes at only finitely many primes; c) there is an α ∈ C {\displaystyle \alpha \in \mathbb {C} } for which the remainder

| ∑ n ≤ x f (n) − α x | {\displaystyle \left|\sum _{n\leq x}f(n)-\alpha x\right|}

is uniformly bounded, as x → ∞ {\displaystyle x\rightarrow \infty }. This equivalent definition of Dirichlet characters was conjectured by Chudakov in 1956, and proved in 2017 by Klurman and Mangerel.