标题： 曼因-德林费尔德定理和雷德迈斯特符号的有理性 显示英文标题

标题： The Manin-Drinfeld theorem and the rationality of Rademacher symbols

摘要： 对于任何非共(compact)的Fuchsian群$\Gamma$，我们证明与尖点余数除子相关的第三类规范微分的周期可以用$\Gamma$的Rademacher符号表示——这是模形式经典理论中出现的周期的推广。 这一结果建立了Rademacher符号与Manin和Drinfeld著名定理之间的关系。 在此基础上，我们提出一个直接的群论论证，以确立Rademacher符号的有理性以及Manin-Drinfeld定理对于新的Fuchsian群和代数曲线族的有效性。 显示英文摘要

摘要： For any noncocompact Fuchsian group $\Gamma$, 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 $\Gamma$ - 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. On this basis, we present a straightforward group-theoretic argument to establish both the rationality of Rademacher symbols and the validity of the Manin-Drinfeld theorem for new families of Fuchsian groups and algebraic curves.