TITLE: sharper minkowski bound
QUESTION [9 upvotes]: If we want to bound the norm of the smallest ideal which generates a nontrivial ideal class, is there a better bound than Minkowski's bound?
(Note that Minkowski's bound is to guarantee something much stronger, namely that every ideal class has a representative whose norm is less than the given bound. Here, we just want that some nontrivial ideal class has such a representative.)

REPLY [6 votes]: The classical reference to an improvement of Minkowski bounds is

R. Zimmert, Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung,  Invent. Math. 62 (1980),  367-380