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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.16738 |
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| _version_ | 1866915169396850688 |
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| author | Besser, Amnon |
| author_facet | Besser, Amnon |
| contents | We describe several instances of the following phenomenon: In bad reduction situations the \( p \)-adic regulator has a continuous and a discrete component. The continuous component is computed using Vologodsky integrals. These depend on a choice of the branch of the \( p \)-adic logarithm, determined by \( \log (p) \). They can be differentiated with respect to this parameter and the result is related to the discrete component. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16738 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regulators and derivatives of Vologodsky functions with respect to log(p) Besser, Amnon Number Theory 11G25 (Primary) 19F27, 11G50 (Secondary) We describe several instances of the following phenomenon: In bad reduction situations the \( p \)-adic regulator has a continuous and a discrete component. The continuous component is computed using Vologodsky integrals. These depend on a choice of the branch of the \( p \)-adic logarithm, determined by \( \log (p) \). They can be differentiated with respect to this parameter and the result is related to the discrete component. |
| title | Regulators and derivatives of Vologodsky functions with respect to log(p) |
| topic | Number Theory 11G25 (Primary) 19F27, 11G50 (Secondary) |
| url | https://arxiv.org/abs/2502.16738 |