In mathematics, the grand Riemann hypothesis is a generalisation of the Riemann hypothesis and generalized Riemann hypothesis. It states that the nontrivial zeros of all automorphic L-functions lie on the critical line ${\displaystyle {\frac {1}{2}}+it}$ with ${\displaystyle t}$ a real number variable and ${\displaystyle i}$ the imaginary unit.

The modified grand Riemann hypothesis is the assertion that the nontrivial zeros of all automorphic L-functions lie on the critical line or the real line.