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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.12114 |
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| _version_ | 1866916811834916864 |
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| author | Cunha, J. Freitas, P. |
| author_facet | Cunha, J. Freitas, P. |
| contents | We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the corresponding zeta functions, which we are then able to solve explicitly. Apart from new applications such as hemispheres, we also believe that the resulting formulae in the cases for which expressions for the determinant were already known are simpler and easier to compute in general, when compared to those resulting from other approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12114 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recurrence formulae for spectral determinants Cunha, J. Freitas, P. Spectral Theory Number Theory 58J50, 58J52 (Primary) 05A10, 11B37, 11B73, 11M41 (Secondary) We develop a unified method to study spectral determinants for several different manifolds, including spheres and hemispheres, and projective spaces. This is a direct consequence of an approach based on deriving recursion relations for the corresponding zeta functions, which we are then able to solve explicitly. Apart from new applications such as hemispheres, we also believe that the resulting formulae in the cases for which expressions for the determinant were already known are simpler and easier to compute in general, when compared to those resulting from other approaches. |
| title | Recurrence formulae for spectral determinants |
| topic | Spectral Theory Number Theory 58J50, 58J52 (Primary) 05A10, 11B37, 11B73, 11M41 (Secondary) |
| url | https://arxiv.org/abs/2404.12114 |