Explicit Bounds for Residues of Dedekind Zeta Functions, Values of L-Functions at s=1, and Relative Class Numbers Original Research Article

We give explicit upper bounds for residues at s=1 of Dedekind zeta functions of number fields, for L(1, χ) for nontrivial primitive characters χ on ray class groups, and for relative class numbers of CM fields. We also give explicit lower bounds for relative class numbers of CM fields (which do not contain any imaginary quadratic subfield). Most of these bounds stem from a useful lemma which enables us to easily obtain neat bounds.