Unconditional results without an unproved hypothesis such as the generalized Riemann hypothesis (GRH) are very weak for an individual number field. But if we consider a family of number fields, one can prove just as strong results as we would assume GRH, in the form: (1) average result in the family; (2) the result is valid for almost all members except for a density zero set. We will explain this philosophy using examples of logarithmic derivatives of L-functions, residues of Dedekind zeta functions, and least primes in a conjugacy class.
