Miyawaki lift

In mathematics, the Miyawaki lift or Ikeda–Miyawaki lift or Miyawaki–Ikeda lift takes two Siegel modular forms to another Siegel modular form. Miyawaki (1992) conjectured the existence of this lift for the case of degree 3 Siegel modular forms, and Ikeda (2006) proved its existence in some cases using the Ikeda lift.

Ikeda's construction starts with a Siegel modular form of degree 1 and weight 2k, and a Siegel cusp form of degree r and weight k + n + r and constructs a Siegel form of degree 2n + r and weight k + n + r. The case when n = r = 1 was conjectured by Miyawaki. Here n, k, and r are non-negative integers whose sum is even.

References

• Tamotsu, Ikeda (2006), "Pullback of the lifting of elliptic cusp forms and Miyawaki's conjecture", Duke Math. J., 131 (3): 469–497, doi:10.1215/s0012-7094-06-13133-2, MR 2219248 
• Miyawaki, Isao (1992), "Numerical examples of Siegel cusp forms of degree 3 and their zeta-functions", Mem. Fac. Sci. Kyushu Univ. Ser. A, 46 (2): 307–339, MR 1195472