Order of Zeros of Dedekind Zeta Functions
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912169435594752 |
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| author | Hu, Daniel Kaneko, Ikuya Martin, Spencer Schildkraut, Carl |
| author_facet | Hu, Daniel Kaneko, Ikuya Martin, Spencer Schildkraut, Carl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_03269 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Order of Zeros of Dedekind Zeta Functions Hu, Daniel Kaneko, Ikuya Martin, Spencer Schildkraut, Carl Number Theory 11R42 (Primary) 20C15 (Secondary) 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. |
| title | Order of Zeros of Dedekind Zeta Functions |
| topic | Number Theory 11R42 (Primary) 20C15 (Secondary) |
| url | https://arxiv.org/abs/2107.03269 |