The well-known Chudakov hypothesis for numeric characters, conjectured by Chudakov in 1950, suggests that finite-valued numeric character h(n), which satisfies the following conditions: 1) h(p) ≠ 0 for almost all prime p; 2) S(x) = Ʃn≤x h(n) = αx + O(1),is a Dirichlet character. A numeric character which satisfies these conditions is called a generalized character, principal if α ≠ 0 and non-principal otherwise. Chudakov hypothesis for principal characters was proven in 1964, but for non-principal ones thus far it remains unproved.
