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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2012.01147 |
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| _version_ | 1866909428607877120 |
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| author | Burrin, Claire |
| author_facet | Burrin, Claire |
| contents | For any noncocompact Fuchsian group $Γ$, we show that periods of the canonical differential of the third kind associated to residue divisors of cusps are expressed in terms of Rademacher symbols for $Γ$ - generalizations of periods appearing in the classical theory of modular forms. This result provides a relation between Rademacher symbols and the famous theorem of Manin and Drinfeld. More precisely, Fuchsian groups whose Rademacher symbols are rational-valued verify the statement of Manin-Drinfeld. We then establish the rationality of Rademacher symbols for various families of Fuchsian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_01147 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Manin-Drinfeld theorem and the rationality of Rademacher symbols Burrin, Claire Number Theory For any noncocompact Fuchsian group $Γ$, we show that periods of the canonical differential of the third kind associated to residue divisors of cusps are expressed in terms of Rademacher symbols for $Γ$ - generalizations of periods appearing in the classical theory of modular forms. This result provides a relation between Rademacher symbols and the famous theorem of Manin and Drinfeld. More precisely, Fuchsian groups whose Rademacher symbols are rational-valued verify the statement of Manin-Drinfeld. We then establish the rationality of Rademacher symbols for various families of Fuchsian groups. |
| title | The Manin-Drinfeld theorem and the rationality of Rademacher symbols |
| topic | Number Theory |
| url | https://arxiv.org/abs/2012.01147 |