The Manin–Drinfeld theorem and the rationality of Rademacher symbols
The Manin–Drinfeld theorem and the rationality of Rademacher symbols
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马宁-德林菲尔德定理和拉德马赫符号的合理性
DOI：
10.5802/jtnb.1225
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Claire Burrin
中科院分区：
文献类型：
--
作者：
Claire Burrin
对于任意非紧的Fuchsian群$\Gamma$，我们证明了与顶点的剩余因子相关的第三类正则微分的周期是用$\Gamma$的Rademacher符号表示的——经典模形式理论中出现的周期的推广。这个结果提供了Rademacher符号与著名的Manin和Drinfeld定理之间的关系。在此基础上，我们给出了一个简单的群论论证，证明了Rademacher符号的合理性以及新的Fuchsian群族和代数曲线的Manin-Drinfeld定理的有效性。
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.
重新审视克罗内克的第一个极限公式
影响因子：
1.2
作者：
Duke, W.;Imamoḡlu, Ö.;Tóth, Á.
通讯作者：
Tóth, Á.