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arXiv · 1601.02672

Extreme residues of Dedekind zeta functions

Peter J. Cho·Henry H. Kim
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Abstract

In a family of $S_{d+1}$-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 $S_5$-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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Peter J. Cho, Henry H. Kim. 2016-01-22. Extreme residues of Dedekind zeta functions. https://doi.org/10.1017/s0305004117000019

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