论文标题
非形态的Ramanujan型的一致性Hurwitz班级
Non-Holomorphic Ramanujan-type Congruences for Hurwitz Class Numbers
论文作者
论文摘要
与所有其他已知的Ramanujan型的一致性相反，我们发现Ramanujan型的一致性可以在非旋律生成系列中支持Hurwitz的班级数字。我们为Hurwitz班级数字的这种非形态一致性建立了分裂结果。我们证明中的两个钥匙工具是Theta系列产品的全体形态投影，其中包括Hurwitz类数字生成系列和Serre定理，这使我们可以排除某些一致性。
In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on non-holomorphic generating series. We establish a divisibility result for such non-holomorphic congruences of Hurwitz class numbers. The two keys tools in our proof are the holomorphic projection of products of theta series with a Hurwitz class number generating series and a theorem by Serre, which allows us to rule out certain congruences.
