Fourier-Jacobi expansion and the Ikeda lift
In 2001 \textit{T. Ikeda} [Ann. Math. (2) 154, No. 3, 641--681 (2001; Zbl 0998.11023)] constructed a lifting from elliptic modular forms to Siegel modular forms of any degree. The existence of such lifting has previously been conjectured by W. Duke and Ö. Imamoglu and by T. Ibukiyama, independently. Since the Ikeda lift is a generalization of the Saito-Kurokawa lift for arbitrary even degree, it is natural to investigate the Fourier-Jacobi coefficients of Siegel modular forms generated by the Ikeda lift. In this article, the author considers such a Fourier-Jacobi expansion of Siegel modular forms generated by the Ikeda lift having two purposes in mind: first, to give an expression of \(L\)-function of certain Siegel modular forms of half-integral weight of odd degree; and secondly, to give a relation among Fourier-Jacobi coefficients of Siegel modular forms generated by the Ikeda lift.
scientific article; zbMATH DE number 5968103
scientific article