Derivatives of Siegel modular forms and modular connections

作者：Yang Enlin^*; Yin Linsheng

来源：Manuscripta Mathematica, 2015, 146(1-2): 65-84.

DOI：10.1007/s00229-014-0687-5

We introduce a method in differential geometry to study the derivative operators of Siegel modular forms. By determining the coefficients of the invariant Levi-Civita connection on a Siegel upper half plane, and further by calculating the expressions of the differential forms under this connection, we get a non-holomorphic derivative operator of the Siegel modular forms. In order to get a holomorphic derivative operator, we introduce a weaker notion, called modular connection, on the Siegel upper half plane. Then we show that on a Siegel upper half plane there exists at most one holomorphic -modular connection in some sense, and get a possible holomorphic derivative operator of Siegel modular forms.

• 出版日期2015-1
• 单位清华大学