标题： 曼宁-德林施泰因定理与雷姆斯彻符号的有理性 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$\Gamma$，我们证明与尖点的剩余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。 更准确地说，其 Rademacher 符号为有理值的 Fuchsian 群满足 Manin-Drinfeld 的陈述。 随后，我们确立了各种 Fuchsian 群族的 Rademacher 符号的有理性。 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. 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.