Riemann hypothesis
Global "L"-functions can be associated to elliptic curves, number fields (in which case they are called Dedekind zeta-functions), Maass forms, and Dirichlet characters (in which case they are called Dirichlet L-functions). When the Riemann hypothesis is formulated for Dedekind zeta-functions, it is known as the extended Riemann hypothesis (ERH) and when it is formulated for Dirichlet "L"-functions, it is known as the generalized Riemann hypothesis (GRH). These two statements will be discussed in more detail below. (Many mathematicians use the label "generalized Riemann hypothesis" to cover the extension of the Riemann hypothesis to all global "L"-functions,