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A Duke-Imamoglu-Ikeda lift is a lift from elliptic modular forms to Siegel modular forms of even degree with respect to the integral symplectic group. An elliptic cusp eigenform of weight $k$ may be lifted to a cusp eigenform of even degree $n$ of even weight $(k+n)/2$.

The Ikeda lifting, also known as Duke-Imamoglu-Ikeda lifting, is a generalization of the Saito-Kurokawa lifting. Given $n\geq1$, it associates to an elliptic modular eigenform $f\in S_{2k}({\rm SL}(2,\mathbb{Z}))$, where $k\equiv n$ mod $2$, a Siegel modular form $F$ of degree $2n$ and weight $k+n$ with respect to the integral symplectic group. The $L$-function of $f$ and the standard $L$-function of $F$ are related by $$ L(s,F)=\zeta(s)\prod_{i=1}^{2n}L(s+k+n-i,f), $$ where $\zeta$ is the Riemann zeta function.

Knowl status:
  • Review status: beta
  • Last edited by Fabien Cléry on 2021-04-27 04:35:17
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