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The (Siegel) Eisenstein series in degree $n$ of even weight $$k>n+1$$ is defined by the formula $\psi_k(Z)=\sum_{(C,D)}\det(CZ+D)^{-k},$ where the summation extends over all inequivalent bottom rows $$(C,D)$$ of elements of the integral symplectic group $${\rm Sp}(2n,\mathbb{Z})$$ with respect to left multiplication by elements of $${\rm GL}(n,\mathbb{Z})$$.

Siegel Eisenstein series are also defined for some subgroups of the full integral symplectic group as well.

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• Review status: beta
• Last edited by Jerry Shurman on 2016-03-29 10:42:08
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