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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.15545 |
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| _version_ | 1866916713138749440 |
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| author | Lynch, Sean B. |
| author_facet | Lynch, Sean B. |
| contents | Lustig gave an infinite product formula for the zeta function of a commutative two-dimensional regular local ring with finite residue field. We extend this to the noncommutative setting with a method based on filtration by an invertible ideal. One application gives an abstract two-dimensional analogue of Hey's formula. Another application provides effective formulae for zeta functions over Rump's two-dimensional regular semiperfect rings. In the appendices, we supplement these two-dimensional applications with requisite one-dimensional calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_15545 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bushnell-Reiner zeta functions over two-dimensional semilocal rings Lynch, Sean B. Number Theory 11R54, 11S45 Lustig gave an infinite product formula for the zeta function of a commutative two-dimensional regular local ring with finite residue field. We extend this to the noncommutative setting with a method based on filtration by an invertible ideal. One application gives an abstract two-dimensional analogue of Hey's formula. Another application provides effective formulae for zeta functions over Rump's two-dimensional regular semiperfect rings. In the appendices, we supplement these two-dimensional applications with requisite one-dimensional calculations. |
| title | Bushnell-Reiner zeta functions over two-dimensional semilocal rings |
| topic | Number Theory 11R54, 11S45 |
| url | https://arxiv.org/abs/2310.15545 |