Miyawaki lift

Not to be confused with Ikeda lift.

The Miyawaki lift or Ikeda–Miyawaki lift or Miyawaki–Ikeda lift, is a mathematical lift that 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