Siegel modular form

Summary

A Siegel modular form is a holomorphic function on the Siegel upper half-space. Under the Siegel modular group $Sp(2g, \Z)$ it transforms by a power of a determinant factor. For $g = 1$ these are the classical modular forms. Siegel modular forms are sections of line bundles on the moduli space of principally polarized abelian varieties. Their Fourier coefficients often encode arithmetic data, such as numbers of representations of one quadratic form by another.