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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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