We discuss the Fourier-Jacobi expansion of certain vector valued Eisenstein series of degree 2, which is also real analytic. We show that its coefficients of index ±1 can be described by using a generating series of real analytic Jacobi forms. We also describe all the coefficients of general indices in suitable manners. Our method can be applied to study another Fourier series of Saito-Kurokawa type that is associated with a cusp form of one variable and half-integral weight. Then, following the arguments in the holomorphic case, we find that the Fourier series indeed defines a real analytic Siegel modular form of degree 2.
|Number of pages||38|
|Journal||Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg|
|Publication status||Published - 2014 Apr|
- Fourier-Jacobi expansion
- Real analytic Eisenstein series
- Skew-holomorphic Jacobi forms
ASJC Scopus subject areas