Power Savings for Counting (Twisted) Abelian Extensions of Number Fields
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929248531382272 |
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| author | Alberts, Brandon |
| author_facet | Alberts, Brandon |
| contents | We prove significant power savings for the error term when counting abelian extensions of number fields (as well as the twisted version of these results for nontrivial Galois modules). In some cases over $\mathbb{Q}$, these results reveal lower order terms following the same structure as the main term that were not previously known. Assuming the generalized Lindelöf hypothesis for Hecke $L$-functions, we prove square root power savings for the error compared to the order of the main term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_03475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Power Savings for Counting (Twisted) Abelian Extensions of Number Fields Alberts, Brandon Number Theory We prove significant power savings for the error term when counting abelian extensions of number fields (as well as the twisted version of these results for nontrivial Galois modules). In some cases over $\mathbb{Q}$, these results reveal lower order terms following the same structure as the main term that were not previously known. Assuming the generalized Lindelöf hypothesis for Hecke $L$-functions, we prove square root power savings for the error compared to the order of the main term. |
| title | Power Savings for Counting (Twisted) Abelian Extensions of Number Fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.03475 |