# sharper minkowski bound

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.)

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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
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