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arXiv · 1207.1756

Derivations of Siegel Modular Forms from Connections

Enlin Yang·Linsheng Yin
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Abstract

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 than a connection in differential geometry. 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.

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Enlin Yang, Linsheng Yin. 2012-07-07. Derivations of Siegel Modular Forms from Connections. https://arxiv.org/abs/1207.1756

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