The Miyawaki lift or Ikeda–Miyawaki lift or Miyawaki–Ikeda lift, is a
mathematical lift that takes two
Siegel modular form
In mathematics, Siegel modular forms are a major type of automorphic form. These generalize conventional ''elliptic'' modular forms which are closely related to elliptic curves. The complex manifolds constructed in the theory of Siegel modular form ...
s to another Siegel modular form. Miyawaki conjectured the existence of this lift for the case of degree 3 Siegel modular forms, and Ikeda
proved its existence in some cases using the
Ikeda lift.
Ikeda's construction starts with a Siegel modular form of degree 1 and weight 2''k'', and a Siegel cusp form of degree ''r'' and weight ''k'' + ''n'' + ''r'' and constructs a Siegel form of degree 2''n'' + ''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
Automorphic forms
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