generalized Riemann hypothesis

This generalization of the Riemann hypothesis to arbitrary Dedekind zeta functions that for any number field $K$, the only zeroes $s$ of the Dedekind zeta function ${\zeta }_K(s)$ that lie in the strip $0\le \mathrm{\Re }s\le 1$ $\mathrm{\Re }s=\frac{1}{2}$.