Extreme residues of Dedekind zeta functions

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  In a family of Sd+1-fields(d = 2,3,4),we obtain the true upper and lower bound of the residues of Dedekind zeta functions except for a density zero set.For S5-fields,we need to assume the strong Artin conjecture.We also show that there exists an infinite family of number fields with the upper and lower bound,resp.
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