Miyawaki lift
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Revision as of 22:17, 8 May 2022 by imported>Rjetedi (update)
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[1] conjectured the existence of this lift for the case of degree 3 Siegel modular forms, and Ikeda[2] 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
- ↑ 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
- ↑ 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
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