On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes
For a number field \(K\), one can improve known explicit bounds of the residue at \(s=1\) of the Dedekind zeta function \(\zeta_K(s)\) by taking into account the factorization behavior of a few small primes. The author shows how this can be applied to obtain better lower bounds for relative class numbers of CM-fields. In particular he deals with the so-called simplest cubic and simplest quartic fields, providing examples of these fields with exceptionally large class numbers. In this way he finds examples of cyclotomic fields with prime conductor and a large plus factor of the class number. Other applications concern imaginary cyclic quartic fields with ideal class groups of exponent 1 or 2 and also some non-abelian fields.
scientific article; zbMATH DE number 5016575
scientific article