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arXiv · 2012.01147

The Manin-Drinfeld theorem and the rationality of Rademacher symbols

Claire Burrin
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Abstract

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.

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Claire Burrin. 2021-03-17. The Manin-Drinfeld theorem and the rationality of Rademacher symbols. https://doi.org/10.5802/jtnb.1225

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