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Extreme residues of Dedekind zeta functions

  • PETER J. CHO (a1) and HENRY H. KIM (a2)
Abstract

In a family of S d+1-fields (d = 2, 3, 4), we obtain the conjectured upper and lower bounds 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 bounds, resp.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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