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STARK ’ S QUESTION AND A STRONG FORM OF BRUMER ’ S CONJECTURE

We show that a question posed by Stark in 1980, regarding abelian L– functions of order of vanishing 2 at s = 0, has a negative answer in the case of characteristic p global fields. We provide links between various versions of Stark’s question and a strong form of Brumer’s Conjecture, in the general context of global fields of arbitrary characteristic. As a consequence, we show that the strong form of Brumer’s Conjecture is in general false for characteristic p global fields.