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Extreme residues of Dedekind zeta functions

Published online by Cambridge University Press:  15 February 2017

PETER J. CHO  and
HENRY H. KIM
PETER J. CHO
Affiliation:
Department of Mathematical Sciences, Ulsan National Institute of Science and Technology, Ulsan, Korea. e-mail: petercho@unist.ac.kr
HENRY H. KIM
Affiliation:
Department of Mathematics, University of Toronto, ON M5S 2E4, Canada, and Korea Institute for Advanced Study, Seoul, Korea. e-mail: henrykim@math.toronto.edu
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Abstract

In a family of Sd+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 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 bounds, resp.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 163 , Issue 2 , September 2017 , pp. 369 - 380
Copyright
Copyright © Cambridge Philosophical Society 2017 

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References

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