Extreme residues of Dedekind zeta functions
Number Theory
2017-10-11 v3
Abstract
In a family of -fields (), we obtain the true upper and lower bound of the residues of Dedekind zeta functions except for a density zero set. For -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.
Keywords
Cite
@article{arxiv.1601.02672,
title = {Extreme residues of Dedekind zeta functions},
author = {Peter J. Cho and Henry H. Kim},
journal= {arXiv preprint arXiv:1601.02672},
year = {2017}
}
Comments
The definition of $L(s,\rho)$ is given in the introduction. The proof of Proposition 4.3 is revised