The Generalized Riemann Hypothesis(GRH) is the assertion that the Riemann Hypothesis is true, and in addition the nontrivial zeros of all Dirichlet $L$-functions lie on the critical line .

Equivalently, GRH asserts that the nontrivial zeros of all degree 1 -functions lie on the critical line.

The Modified Generalized Riemann Hypothesis(MGRH) is the assertion that the Riemann Hypothesis is true, and in addition the nontrivial zeros of all Dirichlet $L$-functions lie either on the critical line or on the real axis.

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