Generalized Riemann hypothesis
The generalized Riemann hypothesis can be stated in the following equivalent forms.
In terms of L-functions
In terms of a particular L-function
All the zeros of the Dirichlet L-function for the Legendre symbol for any prime have real part .
In terms of the prime-counting function
We have the following bound for the modular prime-counting function:
Related facts and conjectures
Other variations of the Riemann hypothesis