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There is an absolute $c>0$ such that the product of the Dirichlet L-functions modulo $q$ has no zero inexcept possibly one zero. If it exists, this exceptional zero $\beta$ is real and simple, belongs to a real nonprincipal character ${\chi }_1$, and lies very close to one. Among the primitive characters whose conductors divide $q$, at most one can have such a zero. This is the Classical zero-free region for Dirichlet L-functions.

An exceptional zero is the possible real simple zero $\beta$ omitted from the otherwise uniform Classical zero-free region for Dirichlet L-functions. It belongs to a real nonprincipal primitive Dirichlet character and satisfies $\beta <1$.