Extreme residues of Dedekind zeta functions

Abstract

AbstractIn a family ofSd+1-fields (d= 2, 3, 4), we obtain the conjectured upper and lower bounds of the residues of Dedekind zeta functions except for a density zero set. ForS5-fields, we need to assume the strong Artin conjecture. We also show that there exists an infinite family of number fields with the upper and lower bounds, resp.