Adelic Rogers' formula and an application
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916104193966080 |
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| author | Alam, Mahbub Strömbergsson, Andreas |
| author_facet | Alam, Mahbub Strömbergsson, Andreas |
| contents | Recently, Seungki Kim proved an extension of Rogers' mean value formula to the adeles of an arbitrary number field. In this paper we give a new proof Kim's formula, and give a criterion ensuring convergence in this formula. We also discuss one application, namely diophantine approximation over imaginary quadratic number fields with congruence conditions, where we prove an analogue of a famous counting result of W. M. Schimdt. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adelic Rogers' formula and an application Alam, Mahbub Strömbergsson, Andreas Number Theory 11Hxx, 11Jxx Recently, Seungki Kim proved an extension of Rogers' mean value formula to the adeles of an arbitrary number field. In this paper we give a new proof Kim's formula, and give a criterion ensuring convergence in this formula. We also discuss one application, namely diophantine approximation over imaginary quadratic number fields with congruence conditions, where we prove an analogue of a famous counting result of W. M. Schimdt. |
| title | Adelic Rogers' formula and an application |
| topic | Number Theory 11Hxx, 11Jxx |
| url | https://arxiv.org/abs/2401.13476 |