论文标题
Manin-Drinfeld定理和Rademacher符号的合理性
The Manin-Drinfeld theorem and the rationality of Rademacher symbols
论文作者
论文摘要
对于任何非共同的fuchsian $γ$，我们表明，与牙齿残留的第三种相关的规范差异的时期是用$γ$的rademacher符号表示的 - 在模块化形式的经典理论中出现的时期的概括。该结果提供了Rademacher符号与著名的Manin和Drinfeld定理之间的关系。更确切地说，Rademacher符号是理性价值的Fuchsian群体验证了Manin-Drinfeld的陈述。然后，我们为紫红色群体的各个家庭建立了Rademacher符号的合理性。
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.
