Abstract :
Explicit bounds are given for the residues at s=1 of the Dedekind zeta functions of number
fields. As a consequence, a simple proof of the Brauer–Siegel theorem and explicit lower bounds
for class numbers of number fields are obtained. Compared with Stark’s original approach, the
paper is explicit and more satisfactory for number fields containing quadratic subfields. Examples
are given of fully explicit lower bounds for class numbers of various types of number fields, for
example normal and non-normal number fields of odd degree, with an emphasis on cubic fields,
real cyclic quartic number fields, and non-normal quartic number fields containing an imaginary
quadratic subfield.
