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arXiv · 2107.03269

Order of Zeros of Dedekind Zeta Functions

Daniel Hu·Ikuya Kaneko·Spencer Martin·Carl Schildkraut
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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 $\operatorname{Gal}(L/K)$ has an irreducible representation of degree at least 3, as predicted by the Artin holomorphy conjecture.

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Daniel Hu, Ikuya Kaneko, Spencer Martin, Carl Schildkraut. 2021-07-22. Order of Zeros of Dedekind Zeta Functions. https://doi.org/10.1090/proc%2F16041

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