Order of Zeros of Dedekind Zeta Functions

DOI10.1090/PROC/16041arXiv2107.03269MaRDI QIDQ6372214

Carl Schildkraut, Spencer Martin, Daniel Hu, Ikuya Kaneko

Publication date: 7 July 2021

Abstract: Answering a question of Browkin, we provide a new unconditional proof that the Dedekind zeta function of a number field $L$ has infinitely many nontrivial zeros of multiplicity at least 2 if $L$ has a subfield $K$ for which $L/K$ is a nonabelian Galois extension. We also extend this to zeros of order 3 when $operatornameGal(L/K)$ has an irreducible representation of degree at least 3, as predicted by the Artin holomorphy conjecture.

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) Zeta functions and (L)-functions of number fields (11R42)

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