Ikeda lift


In mathematics, the Ikeda lift is a lifting of modular forms to Siegel modular forms. The existence of the lifting was conjectured by W. Duke and Ö. Imamoḡlu and also by T. Ibukiyama, and the lifting was constructed by. It generalized the Saito–Kurokawa lift from modular forms of weight 2k to genus 2 Siegel modular forms of weight k + 1.

Statement

Suppose that k and n are positive integers of the same parity. The Ikeda lift takes a Hecke eigenform of weight 2k for SL2 to a Hecke eigenform in the space of Siegel modular forms of weight k+n, degree 2n.

Example

The Ikeda lift takes the Delta function to the Schottky form, a weight 8 Siegel cusp form of degree 4. Here k=6 and n=2.